







Two integers X and Y are selected at random 
20181231 

From Kenneth: Two integers X and Y are selected at random from the integers
1 to 8.If the same integer may be selected twice,find the probability
that;
1)XY=2
2)XY is 5 or more
3)X is greater than Y Answered by Penny Nom. 





Two spinners 
20180813 

From Atina: A spinner has four equal sectors and a number is written on each sector; 1, 2, 3 and 4. A twodigit number is formed by spinning two times. The number on the first spinning makes the first digit and the number on the second spinning makes the second digit. For example, 2 on the first spinning and 1 on the second spinning make the number 21.
(a) Give the sample space S for the experiment.
(b) Consider the following events : E = odd number; F = number smaller than 35; G = prime number.
Give the subset of outcomes in S that defines each of the events E, F, and G.
(c) Describe the following events in terms of E, F, and G and find the probabilities for the events.
• getting an even integer less than 35.
• getting an odd number or an prime.
• getting an even number greater than or equal to 35 that is a prime number. • an odd number smaller than 35 that is not a prime number.
(d) Are E and F mutually exclusive events? Give a reason for your answer. Answered by Penny Nom. 





A probability question concerning eggs 
20161016 

From Brian: Two participants are alternatively selecting eggs from a basket of 6 hardboiled eggs and 6 uncooked eggs.
Alternatively they are smashing the eggs on their foreheads. One participant gets 4 hard boiled eggs in a row and the other person gets 4 uncooked eggs in a row.
What is the probability of this occurring (I watched this happen).
Thank you
Brian Answered by Penny Nom. 





Pizza delivery 
20160403 

From Andrew: Suppose you own a local pizza restaurant, Pizza with Pizzazz, and in order to compete with the big pizza chains in your area you are considering an advertising campaign offering customers a free pizza if their pizza is not delivered in 30 minutes or less. Even though your pizza restaurant is known for its fast and friendly delivery service, you are not sure if you can afford to give away too many pizzas for free. Looking over your past 12,421 pizza deliveries you find out 97% of the pizzas were delivered in 30 minutes or less.
Calculate the probability that all 100 randomly selected pizza deliveries will have been made in 30 minutes or less? Hint: Use the multiplication rule. (Round 4 decimals)
I'm really stumped on how exactly to do this problem. I don't need the answer just the steps broken down to show me how to get it!
It would be gladly appreciated if you could help! Answered by Penny Nom. 





A 13 game bet 
20160228 

From farah: I'm trying to calculate the odds of a 13 game bet. Each game has 2 teams with 3 possible outcomes (win,draw,lose).
What are the odds. Answered by Penny Nom. 





How can the probability be zero? 
20151013 

From anagha: Hi,
thank you for answering (beforehand)
The other day I was just thinking of circles and I came across this peculiar thing.
Most of'em say that there are infinite number of points on the circumference.
and, if it is true, if we spin the radius, the probability that it will point a a particular point is 1/infinity, right?
It didn't make any sense to me and so, I thought there might be an explanation or something of the kind...? Answered by Harley Weston. 





Mathematics 
20151013 

From anagha: Hi,
thank you for answering (beforehand)
The other day I was just thinking of circles and I came across this peculiar thing.
Most of'em say that there are infinite number of points on the circumference.
and, if it is true, if we spin the radius, the probability that it will point a a particular point is 1/infinity, right?
It didn't make any sense to me and so, I thought there might be an explanation or something of the kind...? Answered by Harley Weston. 





A conditional probability problem 
20150824 

From Faustina.: Please I have an exam tomorrow. And I have tried by best in solving this Question. An urn contains 10 white, 5 yellow and 10 black marble. A marble is chosen at random from the urn and it is noted that it is one of the black marble, what is the probability that it is yellow? Answered by Penny Nom. 





A probability question 
20150819 

From Omar: Hi my name omar ,
I have an exam tomorrow and i want answer of this question
Thank you
Q:the probability distribution function of a discrete random variable X is given by
P(X=x)=kx^3
For X=0,1,2,3
a)the value of the constant k . Answered by Penny Nom. 





Another conditional probability problem 
20140608 

From PAVITHRA: Two dice are thrown. What is the probability that sum of the numbers appearing on the die is eleven, if five is appear on the first die Answered by Penny Nom. 





A normal distribution problem 
20140419 

From Melanie: This is the question:
The lifetime of a certain type of car tire are normally distributed. The mean lifetime of a car tire is 40,000 miles with a standard deviation of 5,000 miles. Consider a sample of 10,000 tires. A) How many tires would you expect to last between 35,000 and 45,000 miles? b) How many tires would you expect to last between 30,000 and 40,000 miles? c) How many tires would you expect to last less than 40,000 miles? d)How many tires would you expect to last more than 50,000 miles? e) How many tires would you expect to last less then 25,000 miles? f) What tires would you want on your car and explain your reasoning
Not at all sure that we've done any of this correctly and not sure how to determine how many tires will last less than 25,000 miles.
Any help is appreciated. Answered by Penny Nom. 





A conditional probability problem 
20140413 

From Chiluya: Two fair dice are rolled. what is the probability that the number on the first die was at least as large as 4 given that the sum of the two dice was 8? Answered by Penny Nom. 





Selecting a card 
20140216 

From Akarsh: Cards numbered 1 to 1000 were put in a box.Ali selects cards at random.What is the probability that Ali selects a card containing at least one'3'? Answered by Penny Nom. 





Admiring handblown glass ornaments 
20131121 

From Ruby: We are admiring hand blown glass ornaments 5% are
unmarketable due to defects what is the probability the 3rd
ornament is the first defective one Answered by Penny Nom. 





A contest with 31 people 
20130906 

From Kevin: There is a contest with 31 people and only one winner each week.
We play for 17 weeks.
What are the odds of winning at least one week?
The chances of winning each week are independent from previous weeks. Answered by Robert Dawson. 





Dice 
20130514 

From Julia: What is the probability of rolling(as many times as necessary) a die and getting a total number(sum) when all the rolls are added together of 11? Answered by Lorraine Dame. 





What is the probability that the sixth draw will be a red ball? 
20121123 

From Patty: The probability of drawing a red ball out of a bag containing one red ball and one black ball is 1/2. An experiment is conducted where these two balls are placed in a bag before drawing a ball out. A ball is drawn 5 times from the bag containing the two balls. Each of the first five times the red ball was drawn out. what is the probability that the sixth draw will be a red ball? Answered by Penny Nom. 





More on marbles in a jar 
20120927 

From josh:
Question from josh, a student:
Suppose you have a jar containing 100 red marbles and 100 white marbles. A) If you draw 5 marbles in a row, throwing each marble across the room as you draw it, what is the probability that at least one of them was red? B) If you draw 101 marbles in a row, throwing each one across the room as you draw it, now what is the probability that at least one of them was red?
I saw that this answer was already answered but "The probability that at least one is red is 1 minus the probability that they are all white." makes no sense to me can you please explain i thought that each time a marble is taken out the amount left is different can you please explain better Answered by Robert Dawson. 





Expected value 
20120825 

From melanie: The probabilities are 0.24 , 0.35 , 0.29 , and 0.12 that a speculator will be able to sell a subdivision lot within a year at a profit of P120, 500 , at a profit of P80,000 , at a profit of P40,000 , or at a lost of P60,000 respectively . What is his expected profit ? Answered by Penny Nom. 





Probability 
20120823 

From Christine: In a study of alcoholics, it was found out that 40% had alcoholic fathers and 6% had alcoholic mother. Fourtytwo percent had at least one alcoholic parent. What is the probability that a randomly selected alcoholic will ... Answered by Penny Nom. 





The difference of the numbers on two dice 
20120819 

From dilys: Two fair dice are thrown. Find the probability that the difference of the two numbers is divisible by 4? Answered by Chris Fisher and Lorraine Dame. 





Probability and curling rings 
20120716 

From Fatima: In the olympic event of curling, the scoring area consists of four concentric circles on the ice with radii of 6 inches,
3 feet, 4 feet, and 6 feet
If a team member lands a (43 pound) stone randomly within the scoring area, find the probability that it ends up centred on
a.red b.white c.blue
I am explaining the figure also in words
The smallest Circle is of White color then a blue colour circle then again a White colour circle then the last big circle of red color
The answer for a bit is 5/9
I tried it with many ways but I am not getting the answer
Please clearly tell me what is n(S)and what is n(E). Answered by Penny Nom. 





Six people divided into three groups of two 
20120709 

From Fatima: Six people call them A,B,C,D,E,F are randomly divided into three groups of two,find the probability of the below event(do not impose unwanted ordering among groups)
E andF are in the same group
I solved it but I have a doubt that it is wrong .
My answer is 576
Please help to solve this problem. Answered by Lorraine Dame and Penny Nom. 





Finite probability 
20120708 

From Fatima: Tamika selects two different numbers at random from the set{8,9,10}and adds them.Carlos takes two different numbers
at random from the set {3,5,6}and multiplies them.What is the probability that Tamika's result is greater than Carlo's result Answered by Penny Nom. 





A normal distribution problem 
20120513 

From Alysia: The scores on a test taken by 1000 students are normally distributed with a mean of 66 and standard of deviation of 12. If the college wishes only the top 8% of people to get an A, what would the cutoff score be for the A's? Answered by Penny Nom. 





A uniform probability density function 
20120326 

From Noeline: The label on a bottle of liquid detergent shows contents to be 12 ounces per bottle. The production operation fills the bottle uniformly according to the following probability density function:
f(x) = 8 for 11.975 ≤ x ≤12.10
and
f(x) = 0 elsewhere
a. What is the probability that a bottle will be filled with 12.02 or more ounces?
b. What is the probability that a bottle will be filled between 12 and 12.05 ounces?
c. Quality control accepts production that is within .002 ounces of number of ounces shown on the container label. What is the probability that a bottle of this liquid detergent will fail to meet the quality control standard? Answered by Penny Nom. 





Forming a triangle from 3 line segments 
20120315 

From rustom: A point X is selected at random from a line segment AB with midpoint 0. Find the probability that the line segments AX, XB, and A0 can form a triangle. Answered by Penny Nom. 





Probability 
20120314 

From tom: Let A and B be events with p(A ∪ B)= 7/8, p(A ∩ B)= 1/4, p(A' )= 5/8
Find:
a. p(A)
b. p(B)
c. P(A ∩ B')
...problem for me is that if p(A') = 5/8 then P(A) should be 1/4...so that the p(A' ∪ A) = p(A ∪ B) = 7/8...however, the book says the answer for p(A) is 3/8...does that mean, my interpretation is wrong (because if it is, then all my answers would be crap)...or is it just another typographical error? Answered by Penny Nom. 





Expected value 
20120224 

From Lara: A life insurance company sells a $250,000 1year term life insurance policy to a 20yearold male for $350. According to the National Vital Statistics Report the probability that the male survives the year is 0.998734. Compute and interpret the expected value of this policy to the insurance company.
I'm very confused on how to do this. I assume x is the profit the insurance company makes in the year of $350 but beyond that I don't know what to do. Thanks. Answered by Penny Nom. 





Rolling three dice 
20120126 

From Aishwarya: A red, a blue and a green die are all thrown at the same time. Display all the possible outcomes in a suitable way. Find the probability of obtaining:
1. A total of 18 on the three dice
2. a total of 4 on the three dice
3. a total of 10 on the three dice
4. a total of 15 on the three dice
5. a total of 7 on the three dice
6. the same number on each die.. Answered by Robert Dawson. 





Lotto tickets 
20120103 

From Ashley: Hi. I play the lotto a lot, and have yet to win. How many combinations can I make with 6 numbers 153? I am trying to come up with a dollar amount so I know how much I would have to spend to guarantee a win. Thank you in advance. (I'm no good at math) Answered by Robert Dawson and Penny Nom. 





Drawing three coins from 10 coins 
20110929 

From Michelle: Three coins are chosen at random from a purse containing 6 dimes & 4 quarters. What is the probability that the selection will contain at least one quarter? Answered by Penny Nom. 





A coin toss game 
20110829 

From Aniish: A and B alternately toss a coin.The first one to turn up a head wins.If no more than 5
tosses each are allowed for a single game,find the probability that the person who tosses
first will win the game?What are the odd's against A losing if she goes first? Answered by Penny Nom. 





Two piles of cards 
20110709 

From maribie: a standard deck of playing cards contains 26 black cards and 26 red cards, or 52 cards in all. a deck is randomly divided into two unequal piles, such that the probability of drawing a red card from the small pile is 1/3. at the same time, the probability of drawing a black card from the larger pile is 5/14. how many cards are in the larger pile? Answered by Penny Nom. 





Four digits are to be randomly selected 
20110120 

From sarahbear: Suppose four digits are to be randomly selected (repetitions allowed) Find the probability that
A. 5562 is selected
B.0000 is selected
C. All four digits are the same
D. 2 is the first digit selected Answered by Penny Nom. 





Standard Deviation from a Proportion 
20100608 

From silvestre: A large company finds that approximately 17% of all purchases are returned for credit. If the company sells 100,000 different items this year, about how many items will be returned. Find the Standard Deviation. Answered by Janice Cotcher. 





A probability tree 
20100520 

From Sandy: Children’s meals are being prepared for a large gathering. There is an equal number of chicken, hamburger, and fish meals. Each meal comes with a toy: a ball, a parachute toy, or a Frisbee. There are twice as many balls as Frisbees and an equal number of parachutes and Frisbees.
Use a probability tree to show the sample space and determine the probability that a meal consists of chicken or fish and comes with a ball as a toy. Answered by Penny Nom. 





One red ball and one black ball 
20100411 

From Sammy: The probability of drawing a red ball out of a bag containing one red ball and one black ball is ½. An experiment is conducted where these two balls are placed in a bag before drawing a ball out. A ball is drawn five times from the bag containing the two balls. Each of the first five times the red ball was drawn out. What is the probability that the sixth draw will be a red ball? Explain your answer. Answered by Penny Nom. 





Conditional probability 
20100326 

From Sandy: In a certain school, it is known that 80% of the students use the internet for school projects, 60% use email on a regular basis, and 90% use the internet for school projects or for email on a regular basis. A student from this school is selected at random
Determine the probability that the student used email, given that the student used the internet for school projects.
Sandy Answered by Penny Nom. 





Binomial probability 
20100319 

From Rana: According to one study, it has been claimed that 65% of all single men in Montreal would welcome a
woman taking the initiative in asking for a date. You decide to challenge this study by performing a little
experiment of your own. You randomly select 15 single men from around Montreal and ask them if they
would be comfortable with a woman asking them out for a date. If the claim made by the study was
true, what is the probability that:
a) Exactly 9 men would say yes?
b) Exactly 6 men would say no?
c) More than 11 men would say yes?
d) At most 4 men would say no? Answered by Penny Nom. 





Selecting 3 students from 16 
20100309 

From amper: A class has 12 boys and 4 girls. If three students are selected at random from the class,
what is the probability that they are all boys? Answered by Penny Nom. 





The binomial distribution 
20100227 

From Jessica: A small mobile phone retailer has found that one of their phones has a 12% probability of being faulty and a replacement having to be provided for the customer. They have just
received a trial order for 10 phones from their biggest customer who will take their business elsewhere if 20% or more items are faulty.
i) what is the probability that they will lose their biggest customer? Answered by Penny Nom. 





Four dots are randomly placed on an 8x8 grid 
20100226 

From bobbym: Four dots are randomly placed on an 8x8 grid, compute the probability
that no row or column contains more than one dot. Answered by Claude Tardif. 





The test for some disease is 99% accurate 
20100224 

From baaba: Assume that the test for some disease is 99% accurate. If somebody tests positive for that disease, is there a 99% chance that they have the disease? Answered by Chris Fisher. 





Probability, counting and cards 
20100115 

From Julie: Hello,
 Select a card from the deck(card deck of 52 cards). Place the card back in the deck. What is the probability that both cards will be black? Is it 25/104, 24%?
 Select a card from the deck. Do not replace the card. Select another card. What is the probability that a red and a face card are the two cards you selected? Is it 2/221, .9%?
 Remove the red cards from the deck and assume that the remaining cards have been shuffled: select a card from the remaining deck. Place the card back in the deck. Select another card. What is the probability that both cards will be black? Is it 26/26 x 26/26= 1 x 1 = 1 , 100%?
Select a card from the remaining deck. Do not replace the card. Select another card. What is the probability that a red 3 and a face card are the 2 cards you selected? Is it 0/26 x 6/26 = 0, 0%?
 Seperate 12 face cards from the rest of the deck. Assume that the face cards have been shsuffled. Select 3 cards from the pile of face cards. How many different arrangements can be made by selecting 1 of each card (jack, king, queen) from the pile? is it 1/4 x 1/4 x 1/4 x 1/4 = 1/64?
 How many different ways are there of selecting the queen of clubs, then the king of diamonds, and then the jack of hearts from the pile? Is it 1/12 x 1/12 x 1/12 = 1/1728?
Answered by Robert Dawson. 





The 3ball lottery 
20091209 

From Lee: A friend and I are trying to calculate the odds of choosing the winning
numbers in the 3ball lottery (3digits 09).
We realize that there are 720 Permutations and 120 possible Combinations
of said lottery, but we're having trouble figuring how to determine the
"odds" or probability of winning (1) when order matters, and (2) when it
doesn't. Please help! Answered by Penny Nom. 





A single die is rolled twice 
20091103 

From Michelle: A single die is rolled twice. Find the probability of getting two numbers whose sum exceeds 5.
I can't seem to come up with any of these answers, Help. A. 0.72 B. 0.89 C. 0.68 D. 0.58 Answered by Penny Nom. 





A lottery question 
20091101 

From munirah: assume the chances of winning the lottery are 1 in 1000.how many times would you have to play to attain 0.5 probability of winning at least once? Answered by Robert Dawson and Claude Tardif. 





Probability 
20090927 

From Ed: My mother died 3 years to the day after her daughter died. what are the odds of that happening by chance? thanks Answered by Chris Fisher. 





Toss a coin and roll a die 
20090921 

From Celeste: Can you please tell me how to set up this problem to find the answer. I know they are independent from there I don't know.
a coin and a regular sixsided die are tossed together once. What is the probability that the coin shows a head or the die has a 5 on the upward face? Answered by Penny Nom. 





Probability: selecting students in a particular order 
20090921 

From Rajshri: A class has 100 students with roll numbers 1 to 100. Six students are selected, one after another, at random to form a team. Find the probability that the roll numbers of first three students selected are in ascending order and the roll numbers of the last four students selected are in descending order. Answered by Robert Dawson. 





Airline overbooking 
20090903 

From Nikita: An airline company knows that 8% of it's passengers will not show up for their scheduled flights. A plane has 175 seats.
a) What is the probability that 10 passengers or fewer will not show up?
b) What is the probability that 10 to15 passengers will not show up?
c)What is the probability that exactly 10 passengers will not show up?
d) What is the probability that more than 19 passengers will not show up? Answered by Robert Dawson. 





Tossing a penny 26 times 
20090804 

From Basma: Jack is going ot toss a penny 26 times.
How many times should it land on heads? Answered by Robert Dawson. 





Probability of Two Independent Events 
20090607 

From Sharon: A basketball player is given 2 freeshots, if the probability of making 1 of the 2 shots is 3/4 what is the probability of making 2 of the 2 shots or both shots? Answered by Janice Cotcher. 





Conditional probability 
20090601 

From Tanja: A biased coin where P(heads) =3/5 is flipped 4 times. What is the probability of getting at least 3 heads given at least 1 heads is flipped?
I can calculate this using P(AB) =P(AandB)/P(B) but I've had students asking me how you would work this question out the "long way"
without the formula. I'm am unsure about how you do this the long way. Answered by Robert Dawson. 





A box contains two white socks and two blue socks 
20090520 

From Phu: a box contains two white socks and two blue socks. Two socks are drawn at random. What's the probability that they are match the same color Answered by Penny Nom. 





5 spades 
20090515 

From Dee: From a standard deck of 52 cards, how many cards would you have to draw, without looking at them , to be absolutely certain (a probability of 1) that you had 5 spades? Answered by Robert Dawson. 





Rolling a six on the sixth roll 
20090504 

From Scott: What are the odds of rolling a die 6 times in a row and rolling a 6 only on the 6th try, but not any other time? And how is this calculated? Answered by Harley Weston. 





Two dice and the difference of squares 
20090421 

From dave: I dont understand how to do this: Two fair dice are rolled. What is the probability that the difference of the squares of the numbers is divisible by three? the answer is 5/9 Answered by Harley Weston. 





Expected value 
20090411 

From jp: you pay $.50 and pick a fourdigit number. The state chooses a fourdigit number at random and pays you $2500.00 if your number i chosen. What are the expected winnings from a $.50 Pick 4 wager? Answered by Stephen La Rocque and Harley Weston. 





Choosing a 4 digit number at random 
20090324 

From shabkhal: If a fourdigit number is chosen at random, what is the probability that the product of the digits is 12. Answered by Harley Weston. 





What is the probability of accepting the box? 
20090322 

From x: a box consists of 10 light bulbs inspected by the following procedure: 2 bulbs are chosen at random without replacement. the box is only accepted if both bulbs work. suppose that the box contains 1 defective bulb. what is the probability of accepting the box? Answered by Penny Nom. 





The odds against drawing a red queen 
20090315 

From tabyia: 7. The common deck of 52 cards has 26 black cards (13 spades and 13 clubs) and 26 red cards (13 hearts and 13 diamonds). Each suit consists of ace, king, queen, jack, ten, nine, eight, seven, six, five, four, three and deuce. 13in all.
A single card is chosen at random. Find the odds against its being a red queen?
How many cards will I have to draw to be absolutely certain that I have drawn three black cards Answered by Harley Weston. 





A normal distribution problem 
20090313 

From jude: Regarding the time it takes for an oil change has a normal distribution with a mean of 17.8 minutes and std. deviation of 5.2 minutes. A free oil change will be given to any customer that must wait beyond the guaranteed time. If they don't want to give more than 1% of its customers free oil changes how long should the guarantee be (to the nearest minute). Thank you. Answered by Robert Dawson. 





Probability 
20090312 

From jude: ) Assuming that the heights of boys in high school basketball are normally distributed with a mean of 70 inches and a std dev. of 2.5 inches, how many boys in a group of 100 are expected to be 75 inches tall.
2) Past records from a bank show that the probability of being approved in the written application for hire is 0.63. Then the probability of being approved by the interview committee is 0.85, given that the candidate has been approved on the written application. What is the probability that a person will be approved on both the written application and the interview? Answered by Robert Dawson. 





Dependent & Independent Events 
20090306 

From maci: what is the probablility of drawing at random 2 blue marbles in a row
if there is 3 red,4 green,2 yellow,and 5 blue marbles? Answered by Janice Cotcher. 





The variance 
20090209 

From Ashley: what is the varinace of these scoress 53,67,43,54,58,54,47,35,45,56,45,47,54 Answered by Harley Weston. 





A die is loaded so that... 
20090130 

From Larry: Hi. I'm having trouble solving this problem. Would you be kind enough to point me in the right direction?
A die is loaded so that the probability of a particular face rolling up is proportional to the number of dots
on the face. In other words, getting a six is three times as probable as getting a two. what is the probability
of getting an even number in one toss? Answered by Victoria West. 





Will Juanita be late for class? 
20090128 

From safdar: juanita bumps into tory in the hallway between period 1 and 2,there is a 45% chance that she will be late for class.if she does not bump into tory, she will make it to class on time. there is a 25% chance that juanita will bump into tory. what is the probability that she will be late on any given day. be sure to introduce your events for this question and show the appropriate formula given the events. Answered by Penny Nom. 





25 names in a hat 
20090126 

From Irfan: If there are 25 names in a hat, 15 girl's names and 10 boy's names, what is the probability that a name drawn at random will be
I. a girl's name
II. a boy's name
III. not a girl's name
IV. not a boy's name. Answered by Robert Dawson. 





Probability and birthdays 
20090122 

From La: Neglecting the effect of leap years, what is the chance that, of 6 people selected at random, 2 will have the same birthday? Answered by Penny Nom. 





Does probability apply here? 
20090115 

From Paul: Suppose I have a dice in my hand that I am about to roll. The probability that I roll a six is, all things being equal, 1/6. I accept that.
Suppose now the I roll the dice and immediately cup my hand over the result. What is the probability that I have rolled a six? People seem to want to say it is still 1/6. But it can't be can it!? It is surely either 1 or 0, depending on whether I have in fact rolled a six? Answered by Robert Dawson. 





A seven card poker hand 
20090112 

From Sean: from a standard card deck, seven cards are chosen at random.
find the probability that the set chosen contains exactly three of each
of two different face values.
the second part of the problem asks the probability that the card hand contains
exactly three 2's and exactly three 5's. Answered by Robert Dawson. 





Numbers or Percentage or probability or what? 
20090107 

From Chew: Teacher A teaches 50 students and 45 of them obtained straight As.
Teacher B teaches 5 students and 5 of them obtained straight As.
Which teacher would you send you child to and why? Answered by Robert Dawson and Harley Weston. 





There are 30 marbles in a bag 
20081121 

From Cori: There are 30 marbles in a bag. Twice as many red, as blue, and 1 more green than there are red. What is the probability that when one is pulled out, it will be red? Answered by Penny Nom. 





The distribution of sample sums 
20081121 

From Mark: For large samples, the sample sum (Σ x) has an approximately normal distribution.
The mean of the sample sum is n*μ and standard deviation is (σ*√n). The distribution of savings per account for savings and loan institution has a mean equal to $750 and a standard deviation equal to $25. For a sample of 50 such accounts, find the probability that the sum in the 50 accounts exceeds $38,000. Answered by Penny Nom. 





Sigma in a normal distribution 
20081118 

From Justin: Suppose the random variable Y can be described by a normal curve with
Mu=40. For what value of the standard deviation is
P(20 less than or equal to Y less than or equal to 60) = 0.50
Justin Answered by Harley Weston. 





A normal distribution problem 
20081118 

From Mark: Final Averages are typically approximately normally distributed with a mean of 72 and a standard deviation of 12.5.
your professor says that the top 8% of the class will receieve an A, the next 20%, a B, the next 42%, a C and the bottom 12%, an F.
a. What average must you exceed to obtain an A?
b. What Average must you exceed to receieve a grade better than a C?
c. What average must you obtain to pass the course? (you'll need a D or better) Answered by Harley Weston. 





Probability and a pill bottle 
20081115 

From Dana: If a pill bottle contains either a clonazepam or clonidine pill and
then a clonidine pill is added & the botttle is shaken up and a
clonidine pill is "dumped" out, what are the chances a clonazepam pill
remains in the bottle? Answered by Stephen La Rocque. 





Choosing light bulbs from a box 
20081114 

From Annie: A box of light bulbs contains 3 bulbs, two bulbs are defective.
What is the probability of choosing a nondefective bulb and a defective bulb in 2 draws?
What is the probability of choosing 3 defective bulbs followed by a non defective bulb?
What is the probability of choosing first 2 non defective bulbs followed by a defective bulb? Answered by Penny Nom. 





Probability: Marbles in a jar 
20080922 

From Andrea: Suppose you have a jar containing 100 red marbles and 100 white marbles.
A) If you draw 5 marbles in a row, throwing each marble across as you
draw it, what is the probability that at least one of them was red?
B) If you draw 101 marbles in a row, throwing each one across the room
as you draw it, now what is the probability that at least one of them was
red? Answered by Harley Weston. 





A multiple choice exam 
20080913 

From Phalange: A multiple choice exam consists of 12 questions, each having 5 possible answers. To pass, you must answer at least 9 out of 12 questions correctly. What is the probability of passing if:
a. You go into the exam without knowing a thing, and have to resort to pure guessing?
b. You have studied enough so that on each question, 3 choices can be eliminated. But then you have to make a pure guess between the remaining 2 choices.
c. You have studied enough so that you know for sure the correct answer on 2 questions. For the remaining 10 questions you have to resort to pure guessing. Answered by Harley Weston. 





Balls and cubes in an urn 
20080909 

From Dave: In an urn, there are 80 objects of two kinds: cubes (C) and balls (B). An object can be either red (R) or green (G).
Note that all the four combinations are possible and that the number of cubes is not necessarily equal to the number of
balls. Similarly, the number of red objects is not necessarily equal to the number of green objects. Someone tells us that
in the urn there are 20 red cubes, 50 balls, and 30 red objects. An object is randomly selected from the urn.
(a). What is the probability that a green ball is selected?
(b). If we know that a cube has been selected, what is the probability that it's red?
(c). If we know that a red object has been selected, what is the probability that it's a cube? Answered by Harley Weston. 





Microwave ovens and probability 
20080904 

From Vi: A microwave oven manufacturer claims that only 10% of the ovens it makes will need repair in the first year. Suppose three recent customers are independently chosen.
a. If the manufacturer is correct, what is the probability that at least two of the three ovens will need repair in the first year?
b. If at least two of the three customers' ovens need repair in the first year, what inference may be made about the manufacturer's claim? Answered by Harley Weston. 





Overbooking flights 
20080710 

From DON: Overbooking by Airlines
This is a simplified version of calculations used by airlines when they overbook
flights. They realize that a certain percentage of ticketed passengers will cancel
at the last minute. Therefore, to avoid empty seats, they sell more tickets than
there are seats, hoping that just about the right number of passengers show up.
We will assume that the noshow rate is five percent.
For a flight with 220 seats, the airline wants to find how sensitive various
probabilities are to the number of tickets it issues. In particular, it wants to
calculate
a) the probability that more than 225 passengers show up
b) the probability that more than 220 passengers show up
c) the probability that at least 215 seats will be filled
d) the probability that at least 210 seats will be filled.
To assess the benefits and drawbacks of issuing various numbers of tickets on an
airline flight with 220 seats, create a table showing as many different scenarios
as possible (table only on one page when printed) and use a second page for
your analysis and recommendation to the airline. Which are the good cases,
which are the bad cases for the airline? Answered by Janice Cotcher. 





Probability and two digit numbers 
20080707 

From Peter: What is the probability that if you multiply two randomly selected two digit whole numbers, the result is greater that 100 and less than 200. Express your answer as a common fraction. Answered by Janice Cotcher. 





Choosing a number from 1  400 
20080704 

From Peter: The numbers 1400, inclusive, are put into a hat. What is the probability that the first number chosen at random is a multiple of 4 or 17? Express your answer as a common fraction.
How do you do this the question without a calculator? Answered by Leeanne Boehm. 





Probability of Matching Socks 
20080704 

From Peter: Rick has 6 different pairs of socks. Whats the probability that two randomly selected socks will be from a matching pair? Answered by Leeanne. 





Some phone numbers 
20080630 

From star: What do you think the probability of finding the last 3 digits of a telephone number if the 1st digit begins with 7? Answered by Janice Cotcher and Harley Weston. 





The mean and variance 
20080605 

From Donny: An investment will be worth $1,000, $2,000, or $5,000 at the end of the
year. The probabilities of these values are .25, .60, and .15, respectively.
Determine the mean and variance of the worth of the investment. Answered by Harley Weston. 





A coin is tossed 30 times 
20080413 

From seulki: coin tossed 30 times, what is the probability that the heads show up fewer than 17 times? Answered by Harley Weston. 





A normal distribution problem 
20080329 

From Lorie: 3. The amount of annual snowfall in a certain mountain range is normally distributed with a mean of 109 inches, and a standard deviation of 10 inches.
a. What is the probability that the mean annual snowfall during 40 randomly picked years will exceed 111.8 inches? Answered by Harley Weston. 





Probability and Merta trains 
20080327 

From Lorie: 4. Merta claims that 74% of its trains are on time.
a. Find the probability that among the 60 trains, 38 or fewer arrived on time. Answered by Harley Weston. 





A probability distribution 
20080323 

From Lorie: The probabilities that a batch of 4 computers will contain 1, 2, 3, and 4 defective computers are 0.6274, 0.3102, 0.0575, and 0.001 respectively.
a. Set up a probability distribution to describe this situation. Answered by Penny Nom. 





Expected value and standard deviation 
20080319 

From Patrick: Heres a question i cant figure out:
a small airline company has only three flights per day. The number of
delayed flights per day is regarded as a random variable, and I'm
supposed to calculate the expected
value and standard deviation of the number of delays.
the probability distribution looks like:
No. of Delays: 0 1 2 3
Prob. of delay: 05. 0.3 .1 .1 Answered by Harley Weston. 





Probability and hair 
20080308 

From CELESTE: MY BOSS POSED THIS QUESTION TO US. THE FIRST WITH THE CORRECT ANSWER WINS. tHANKS!
In a city of 200,000 people, no one has more than 100,000 hairs on his or her head, and no one will have fewer than 1. What are the chances that two inhabitants have exactly the same number of hairs? (Nose and ear hairs don't count.) Answered by Penny Nom. 





Rolling a 5 before an 11 
20080227 

From Jeremy: If rolling two sixsided dice, what is the probability that a sum of 5 will be rolled before a sum of 11? Answered by Stephen La Rocque and Harley Weston. 





Multiple guess 
20080227 

From debbie: What is the probability of getting 6 out of 10 (a,b,c,d,e) questions correct, by random selection? Answered by Stephen La Rocque. 





All possible arrangements of the word "PROBLEM" 
20080225 

From student: Consider all possible arrangements of the word "PROBLEM". If a word is picked at random, find the probability that
(a) the word starts with a vowel
(b) the word ends with a consonant. Answered by Harley Weston. 





Drawing marbles from a bag 
20080217 

From jan: 9 marbles are placed in a bag. 4 are blue, 3 are green, 2 are red. what is the probability of the following: a)p(g) (b) p(b) (c) p(r or g) Answered by Chris Langdon. 





Three hens 
20080209 

From joan: A farmer has 3 hens. It is determined that each hen lays 6 eggs in one week. a)find the probability that a hen lays an egg in a randomly chosen day b) find the probability that each hen lays an egg in a randomly chosen day. c) find the probability that no hen lays an egg in a randomly chosen day. d) draw a tree diagram to illustrate the number of hens laying an egg in a randomly chosen day.. Answered by Stephen La Rocque. 





Two spinners 
20080205 

From Kim: Zack has two spinners with numbers on them. the probability of spinning
a 7 on both spinners is 3/20. if the probability of spinning a 7 on the first
spinner alone is 1/4 what is the probability of getting a 7 on the second
spinner alone? Answered by Penny Nom. 





Tossing a coin 
20080125 

From Christopher: Jack tosses a coin 30 times. How many times would you expect the coin to land tails side up? Answered by Harley Weston. 





Choosing 10 numbers from 40 numbers 
20080118 

From Antwan: I have 40 numbers........number 140.
I want to know how many times i can chose 10 of those numbers without picking the same exact sequence twice if its even possible? Answered by Stephen La Rocque. 





Conditional probability 
20080114 

From Sara: Hello!
Ian has a photocopier in his office. If the photocopier is working on a certain
day then the probability that it will be working the next day is 0.9.
If the photocopier is not working on a certain day then the probability that
it will not be working the next day is 0.3.
The photocopier is not working on Monday.
(a) Calculate the probability that it will be working on Tuesday and Wednesday.
(b) Calculate the probability that it will not be working on Wednesday.
Could you please draw a tree diagram for this problem. Answered by Penny Nom. 





A binomial probability problem 
20080108 

From rougi: According to statistics of the company about 4% of the people who buy tickets do not arrive to the flight . The company sells 205 tickets to plane that has 200 places . Use the binomial distribution to calculate what is the probability that all the people who come to the flight get a place. Answered by Harley Weston. 





Retail hiring in Britain 
20080103 

From ROGI: major hiring in retail in BRITAIN,ACCORDING TO MORE IN STORE ARE ASFOLLOWS:9,000 AT SAFEWAY; 5000 AT BOOTS; 3400 AT DEBENHAM; AND 1700 AT MARKS AND SPENCER. WHAT IS PROBABILITY THAT THE A RANDOMLY SELECTED NEW HIRE FROM THESE WAS HIRED BY MARKS AND SPENCER? Answered by Penny Nom. 





The case of the forgotten umbrella 
20071225 

From rougi: a lecturer goes to a bar because it looks like raning.he takes an umbrella with him. on the way to bar he forgets the umbrella in the bus with probability 0,1,in the bar with probability 0.3 and on his way home in the taxi with probability 0,6
a)what is probability that he forgets the umbrella on his tripe?
b)when he gets home he realizes that he has forgotten his umbrella,what is probability that he has forgotten it in the taxi? Answered by Stephen La Rocque and Harley Weston. 





The probability of the second win on the third test 
20071221 

From pankaj: Q.The probability of india winning a test match against india is 1/2. Assuming independence from match to match. what is the probability that india's second win occurs at 3rd test in a 5 match series? Answered by Penny Nom. 





Three students, four bars 
20071207 

From rougi: in a certain town, there are 4 different bars and 3 student (independently)decided to go bars :
a)what is probability that these three student go to the same bar (at certain night)?
b) what is probability that these three go to different bars? Answered by Penny Nom. 





6 nickels, 4 dimes, and 2 quarters 
20071202 

From manny: Suppose you have 6 nickels, 4 dimes, and 2 quarters in your pocket. If you draw a coin randomly from your pocket, what is the probability that
a. You will draw a dime? Answered by Penny Nom. 





Blood type probabilities 
20071201 

From Noelle: Question from Noelle, a student:
Blood Type % Population
O+ 37.4%
O 6.6%
A+ 35.8%
A 6.3%
B+ 8.5%
B 1.5%
AB+ 3.4%
AB .6%
I need to make another table showing the probablility of meeting someone in each of the eight blood groups. I'm not sure how to find the probability with percentages. Thanks for your help. Answered by Penny Nom. 





The probability of an odd number 
20071127 

From Malonda: Suppose you select a 3digit number at random from the set of all positive 3digit numbers. Find each probability.
P(odd numbers) Answered by Stephen La Rocque. 





Confidence level 
20071119 

From Fara: It is common for public opinion polls to have a " confidence level" of 95%, meaning
that there is a 0.95 probability that the poll results are accurate within the claimed margins of error.
If six different organizations conduct independent polls, what is the probability that all
six of them are accurate within the claimed margins of error? Does the results suggest that
with a confidence level of 95%, we can expect that almost all polls will be within the claimed
margin of error? Answered by Harley Weston. 





pvalues and tdistributions 
20071113 

From Don: I have a ttest statistic of 1.28 and a degree of freedom of 6.
I know the pvalue is .248 I cannot figure out how to calculate that value.
I have used software to get it but I want to know how to calculate it using
the tdistribution table. Answered by Harley Weston. 





A normal distribution problem 
20071111 

From Jenny: I am a parttime student so that i have no time to ask the lecturer. moreover the book which i borrowed from state library don't have any answer. but i have already done with most of the question. but these three question which i attached is really confusing me. i am very glad that you help me. Answered by Harley Weston. 





Two probability density functions 
20071021 

From ravinder: A program consists of two modules executed sequentially.
Let f1(t) and f2(t) respectively denote the probability density functions
of time taken to execute the two modules. The probability
density function of the overall time taken to execute the program is
given by
(1) f1(t) + f2(t)
(2) INTEGRAL OF(f1(x)f2(x)dx) from 0 to t
(3) INTEGRAL OF(f1(x) f2(tx) dx) from 0 to t
(4) max{f1(t), f2(t)} Answered by Andrei Volodin. 





A multiple choice exam 
20071021 

From jon: a student is taking a multiple choice exam in which each question has four choices.
assuming that she has no knowledge of the correct answers to any of the questions, she
has decided on a strategy in which she will place four balls (marked A, B, C, D) into a box. she randomly
selects one ball for each question and replaced the ball in the box. the marking will determine her answer to the question.
there are five multiple choice questions on the exam. what's the probability that she will ... Answered by Stephen La Rocque and Harley Weston. 





Rolling a die repeatedly (you can't just add percentages) 
20071004 

From Howard: If my son has a 16.66% chance of rolling a particular number on a dice,
and he rolls for it 6 times, he knows (from experience) that his
odds of getting at least 1 right are not 100% (16.66% +16.66%+16.66% etc).
He asked me if there was an equation that would give him the correct
percentage chance of success when trying X times for a Y% chance
of something. Answered by Victoria West. 





The weights of packages are normally distributed 
20070923 

From alan: the weight of a packet of sweets produced in a factory are normally distributed.
the mean weight is 100g
the standard deviation is 2g
all packets weighing less than 99g and more then 105g are rejected
what proportion are rejected Answered by Penny Nom. 





Amy is playing a game 
20070825 

From vanessa: problem statement:
amy is playing a game.
in order to win this game, she has to draw a redcoloured card from a given box.
advise her on her chances of winning. Answered by Penny Nom. 





Combining probabilities 
20070820 

From Arul: Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 1/2 , and 5/8 , respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem ? Answered by Stephen La Rocque. 





The odds of winning a contest 
20070729 

From Kevin: I have been asked by a customer in Missisauga to track down some odds of
winning a contest. In this contest, the last 4 digits of the winner's
driver's license number have to match the last 4 digits of a Harley VIN
number. There are 200 people maximum allowed into the drawing, 10,000 total
possible VIN combos. Would the odds be 1:50 or something other than that? Answered by Harley Weston. 





Guessing multiple choice answers 
20070724 

From carla: You are taking a multiple choice quiz that consist in 3 questions, each question has
3 possible answers only one is correct. To complete the quiz you randomly guess the answer
to each question . Find the probability of guessing exactly 2 answer correctly. b) at least to answer correctly . c)less than two answer correctly Answered by Stephen La Rocque. 





The probability of rolling double sixes twice in a row 
20070710 

From Matt: what is the probability of rolling double sixes twice in a row? Answered by Stephen La Rocque. 





Probability and blood type 
20070615 

From Jim:
Blood Type 
Male 
Female 
Total 
O 
80 
370 
450 
A 
150 
250 
400 
B 
50 
50 
100 
AB 
20 
30 
50 
Total 
400 
600 
1000 
What is the probability that the person selected is female if the person’s blood type is O?
What is the probability that the person selected has blood type AB if the person is male?
What is the probability that the person selected is a female with blood type O? Answered by Penny Nom. 





A probability problem 
20070613 

From Lina: A point P is selected at random from the interior of the pentagon with vertices
A = (0,2), B = (4,0), C = (2 π+1,0), D = (2 π+1,4), and E = (0,4). What is the probability
that Answered by Stephen La Rocque and Penny Nom. 





Probability tree  two switches failing 
20070605 

From Maura: draw a probability to show the outcomes of two new switches (a) of both switches being faulty (b)both switches are not faulty (c) that one switch is faulty. The failure rate is 1/10. Answered by Stephen La Rocque. 





The difference between two dice 
20070602 

From smiley: Two standards dice are rolled. Determine the probability
that the difference between the two numbers on the dice is 2 Answered by Penny Nom. 





The attendance at football games 
20070528 

From cookie: The attendance at football games at a certain stadium is normally distributed, with a mean of 55,000 and a standard deviation of 4,500.
a) What is the probability of the attendance exceeding 60,000?
b) What is the probability of the attendance being between 45,000 and 50,000? Answered by Penny Nom. 





What are the odds that the selections were random? 
20070526 

From alan: An employer must select three people for layoff from three groups. Group 1 has 4 members and the oldest member is selected. Group 2 has 7 members and the oldest member is selected. Group 3 has 2 members and the younger is selected. Assuming equal qualifications, what are the odds that the selections were random vs. biased as to age? What is the formula to determine this? Answered by Penny Nom. 





Probability that a restaurant will succeed 
20070523 

From Cookie: You wish to open a new restaurant and are considering locations in Toronto and Hamilton, but only one location will actually become available. If it is built in Toronto, the restaurant stands an 80% chance of successfully surviving its first year. However, if it is built in Hamilton, its chance of survival falls to 65%. It is estimated that the chance of Hamilton being available is 60% and Toronto being available is 40%. Find the probability that the restaurant will :
a) survive its first year
b) be built in Toronto and survive its first year
c) be built in Hamilton, given that it survived its first year
d) not survive its first year, given that it is built in Toronto
Thanks Answered by Penny Nom. 





Probability tree 
20070519 

From Patrick: My question involves a video game called Guild Wars. In the game you can have modifications(mods) on items. One such mod is that you have a 20% chance to halve the casting time of a spell. You can have 2 of these mods available to you. Now, it is to my understaning that combined, you would have a 32% chance to halve the casting time and a 4% chance to quarter the casting time. Is this correct? Answered by Stephen La Rocque. 





Probability of getting an A 
20070509 

From Christine: In a class of 15 people, exactly 3 got an A. If 2
people are randomly chosen from this class, what is the probability that
at least one of these 2 got an A? Answered by Paul Betts. 





Permutations, probability and standard normals 
20070509 

From Katrina: I have a few problems that i seem to be stuck on or can not start. Can you please help me ?
1) There are 20 people on an event planning committee. How many differnt ways can a
chairperson and assistant to the chairperson be selected?
2) An unprepared student makes random guesses for 10 true or false questions on a quiz.
Find the probability that the student passes the quiz by guessing 7 of the questions
correctly.
3) The heights of 18 year old men are normally distributed with a mean of 68 inches and
a standard deviation of 3 inches. If a random sample of 25 18year old men is selected
what is the probability that the mean height is between 68.5 and 72 inches? Answered by Penny Nom. 





A committee of 4 
20070509 

From Danielle: I was wondering: What is the probability that both Barb and Bob are both
on the same committee of 4 which is chosen fom their class of 10 people?
Is it 2/5? Thanks a bunch! Answered by Penny Nom. 





Probability of H.I.V. tests 
20070507 

From Danielle: A medical test detects H.I.V. Among those who have H.I.V., the test will detect the disease with probability 0.95; among those who do NOT have H.I.V., the test will falsely claim that H.I.V. is present with probability 0.0125. Among those who take this test, 4% have H.I.V. The test is given to Lucille, and indicates that she has H.I.V. What is the probability that Lucille actually has H.I.V.? Answered by Stephen La Rocque. 





Probability 
20070507 

From Danielle: A box contains 3 defective lights and 5 nondefective lights. The lights are tested one at a time without replacement. What is the probability that the 3 defective bulbs will be found in the first 3 tests?
is it 1/56 by chance? Answered by Stephen La Rocque. 





A normal distributiion question 
20070420 

From Erika: The amount of time required for a certain type of automobile transmission repair at a service garage is normally distributed with the mean = 45 minutes and the standard deviation =8.0 minutes. The service manager plans to have work begin on the transmission of a customer’s car 10 minutes after the car is dropped off, and he tells the customer that the car will be ready within one hour total time. What is the probability that he will be wrong? Illustrate the proportion of area under the normal curve which is relevant in this case.
What is the required working time allotment such that there is a 75 percent chance that the transmission repair will be completed withing that time? Illustrate the proportion of area that is relevant. Answered by Penny Nom. 





6 purple and 4 orange socks 
20070412 

From Reane: ^ purple and 4 orange socks. Choose one then choose a second without putting the 1st back. What is the probability of getting 2 purple socks. I can't reach back far enough in my memory to recall how to do this. Answered by Gabriel Potter. 





Determine the probability that the triangle is acute. 
20070410 

From Greg: Points A1, A2, . . ., AN are equally spaced around the circumference of a
circle and N >=3. Three of these points are selected at random and a triangle
is formed using these points as its vertices. If N = 2k for some positive integer
k >= 2, determine the probability that the triangle is acute. Answered by Penny Nom. 





Almost surely 
20070410 

From Ben: what does "almost surely" mean in probability? what's the diff between absolutely certain and "almost surely"?
thx. Answered by Penny Nom. 





Expected value 
20070330 

From Katrina: A term life insurance policy will pay a beneficiary a certain sum of money upon the
death of the policy holder. These policies have premiums that must be paid annually. Suppose a
life insurance company sells a $250,000 oneyear term life insurance policy to a 20yearold male
for $350. According to the National Vital Statistics Report, Vol. 47, No. 28, the probability the
male will survive the year is 0.99865. Compute the expected value of this policy to the insurance
company. Does the company expect to make money at this rate? Answered by Penny Nom. 





A case of wine 
20070330 

From Carol: Suppose 3 of 12 bottles in a case of wine are bad. If you randomly select 2 bottles what is the probability that one is good and one is bad Answered by Penny Nom. 





Colour blindness 
20070329 

From Katrina: 9% of men and .25% of woman can't distinguish between
the colors red and green. This is the type of color blindness
that causes problems with traffic lights. If 6 men are randomly
selected for a study of traffic signal perceptions, find the probability
that exactly two of them cannot distinguish between red and green. Answered by Stephen La Rocque. 





Simplifying an expression in probability 
20070326 

From Natasha: well it is
p(4) =
5!
 X (0.5) ^4 X (1 0.5)^54 = 0.15625
4!(54)!
Now the ^ is to the power of (I believe) Its written in the book as
(10.5)4 (but the 4 is little and on the top right corner of the first bracket
now the second ^54 is also little on the top right corner of the 2nd
bracket.
This is an equation from my text book but for the life of me I cannot figure
out how to solve it. If you can give me step by step procedure I'd
like that. The answer is also there I just don't know how to get to the
answer. Thank you. Answered by Stephen La Rocque. 





The question is whether the games is fair or unfair? 
20070315 

From kk: Players have two red chips each with an A side and a B side, and one blue chip with an A side and a B side.
The players flip all three chips. Player one wins if both red chips show A, if the blue chip shows A, or if all chips show A.
Otherwise player two wins. The Question is: Whether the games is fair or unfair and to draw a probability tree to show the answer.
Hope you can help Answered by Haley Ess. 





How many marbles are Red and how many marbles are White? 
20070313 

From Angie: A jar has 16 marbles in it. Most of the marbles are Red and the rest are
White. Two marbles are taken out of the jar at the same time. It is
equally probable that two marbles are of the same colour as the two
marbles of different colour (that is the probability that they are both red
or both white is the same as they are different). How many marbles are Red and how many marbles are White?
Could anyone help me with the above question?
Best regards,
Angie Answered by Danny Dyer. 





Rolling two dice 
20070306 

From Mary: I have a test and I need to know how to figure out how to find the probability of rolling 2 dice and coming up with a 7 for both rolls. Could you please explain how to find the probability? Thank you. Mary Answered by Penny Nom. 





Mutually exclusive events 
20070301 

From kalyssa: will you me an example of two events that are mutually exclusive and could you explain to me what mutually exclusive means? Answered by Steve La Rocque, Pam Fowler and Penny Nom. 





Find the probability of choosing a red or 5 ball. 
20070117 

From Carl: four red balls numbered 1 thru 4 and three blue balls numbered 3 thru 5 placed in a bag. a ball is drawn from the bag. find the probability of choosing a red or 5 ball. Answered by Stephen La Rocque. 





Probability and Lisa's rings 
20070115 

From Spencer: lisa has 9 rings in her jewelry box. five are gold and 4 are silver. if she randomly select 3 rings to wear to a party, find each probability p(2 silver or 2 gold) Answered by Stephen La Rocque. 





A probability problem 
20070106 

From Rose: The radius of the a small circle is 1 and the radius of the large circle is 2. If two points are selected at random from the interior of the large circle, what is the probability that both points will be from the shaded region? the shaded area outside the small circle. Answered by Penny Nom. 





What is the expected number of ripe and ready to eat watermelons 
20061129 

From James: An agricultural cooperative claims 95 percent of the watermelons shipped out are ripe and ready to eat. If 20 watermelons are shipped out , what is the probability that the number of watermelon that are ripe and ready to is (i) exactly 14 (ii) more than 18 (iii) of the 20 watermelons that are shipped what is the expected number of ripe and ready to eat watermelons Answered by Penny Nom. 





What proportion of cups of coffee have at least one defect 
20061128 

From Ayman: coffee machine may be defective since it dispenses the wrong amount of coffee (C) & or the wrong amount of suger ( S ) the probability of these defects are P(C) = 0.05, P(S) = 0.04 & P( C&S ) = 0.01 find 1 what proportion of cups of coffee have at least one defect 2 what proportion of cups of coffee have no defect Answered by Penny Nom. 





Sally plays roulette 
20061121 

From Sherry: Sally plans to bet 100 bets of $1.00 each on red roulette. the probability of the ball landing on red is 18/38 what is the probability that Sally will win at least half the time Answered by Penny Nom. 





What is the probability that the sum of the two numbers is even? 
20061101 

From Ryan: 10 balls numbered 110 are in a jar. George reaches into the jar and pulls out a ball. Then Wally pulls out another ball. What is the probability that the sum of the two numbers is even? Answered by Haley Ess. 





A specific 8 digit number in a 11 digit mobile phone number 
20061013 

From James: I need to know the chance of finding a specific 8 digit number in a 11 digit mobile phone number.
the number must be 29571596 and the 11 digit phone number must end in this.
All numbers 09 are used in a mobile number but the first 2 digits will always be 07.
Is there a way to work this out?? Answered by Stephen La Rocque. 





My wife's recent pregnancy, 
20060724 

From Tom: During my wife's recent pregnancy, it so happened that my wife's 29th birthday fell on the exact same day that her unborn child was 29 weeks old (i.e. it was 29 x 7 days from the date of conception as advised by the doctor)
I would like to know what the probability is of the above event occurring for a randomly chosen pregnant woman i.e. that the pregnant mum's x'th birthday falls on the same day that the unborn child is x weeks old EXACTLY.
Answered by Stephen La Rocque. 





What is the probability that the policeman will shadow the correct person? 
20060614 

From Kolby: Through an informer from the underworld, the police know the meeting place of a gang. The identity of the different gang members, however, is unknown. it is the duty of a policeman to shadow the leader of the gang. The policeman knows that the leader is the tallest of the five persons, all of whom have different heights. after the meeting, the gangsters, as a safety measure, leave the building separately at intervals of 5 minutes. As the policeman cannot see who is the tallest, he decides to let the first two gangsters go and shadow the one after that who is taller than all those who left before.Through an informer from the underworld, the police know the meeting place of a gang. The identity of the different gang members, however, is unknown. it is the duty of a policeman to shadow the leader of the gang. The policeman knows that the leader is the tallest of the five persons, all of whom have different heights. after the meeting, the gangsters, as a safety measure, leave the building separately at intervals of 5 minutes. As the policeman cannot see who is the tallest, he decides to let the first two gangsters go and shadow the one after that who is taller than all those who left before. What is the probability that the policeman will shadow the correct person? Answered by Steve La Rocque and Claude Tardif. 





Flipping a coin 
20060608 

From John: If a coin is flipped n times, where H is the number of heads after n flips, and T the number of tails, then will the quantity (HT) change signs infinitely often as n goes to infinity? Answered by Chris Fisher. 





A bag contains 9 red, 6 white, 3 blue, and 8 green marbles 
20060518 

From Micheael: A bag contains 9 red, 6 white, 3 blue, and 8 green marbles. Two marbles are drawn, but the first marble drawn is not replaced. Find P(white, then white). Make into one reduced fraction. Answered by Paul Betts and Steve La Rocque. 





A person is given 3 true or false questions 
20060511 

From Larry: A person is given 3 true or false questions. They have no idea of the answers. What is the probability of the person getting them all correct? Could you show me a tree for this. Answered by Penny Nom. 





School bus reliability  a probability question 
20060427 

From Peggy: The school bus arrives at Janet's stop on time on 75% of school mornings. What is the probability it will arrive on time each day in a 5day week? Answered by Stephen La Rocque. 





Oddman out coin tossing and probabilities 
20060427 

From Kalyan: When four people toss fair coins, what is the probability that in a given toss there will be one "odd man". That is one person whose coin does not have the same out comes as that of any other members? Answered by Stephen La Rocque. 





Probability of a committee with 3 parents and 3 teachers 
20060412 

From Javier: A committee consisting of 6 people is to be selected from 8 parents and 4 teachers. Find the probability of selecting 3 parents and 3 teachers. Answered by Stephen La Rocque. 





Probability of getting their stories straight 
20060405 

From Amy: Four students drive to school in the same car. They claim they were late because they had a flat tire. Assuming they did not have a flat tire what is the probability that they all would choose the same tire if asked which one was flat. Answered by Stephen La Rocque. 





Some probability questions 
20060402 

From Amy: I am a student and need help on some probability questions
I really need your help on some problems dealing with probability. If you will show me how to do the following: Answered by Harley Weston. 





Permutations and probability 
20060327 

From Alyssa: I am a high school student, my teacher gave the class a worksheet on permutations and probability and told us to do independent work when we have not covered the material yet and he will not answer any questions. I am lost and don’t know where to begin. Can you help?
1. Find the number of 6letter permutations of all the letters in EUCLID that end with either the letter E or the letter D?
Aluminum chips A, B. C, and D weigh 1g. 5g. 10g. and 20g. respectively. How many different masses can be measured by using one or more of the 4 weighs on a balance scale? Answered by Stephen La Rocque. 





A manufacturer of cotton pins 
20060320 

From Nirmal: A manufacturer of cotton pins knows that 5% of his products are defective. If he sells cotton pins in boxes of 100 and guarantees that not more than 10 pins will be defective, what is the approximate probability that a box will have the guaranteed quantity? Answered by Penny Nom. 





A hat contains between 10 and 25 marbles 
20060306 

From Kerry: A hat contains between 10 and 25 marbles. Some marbles are green, and the rest are yellow. Without looking you are to reach into the hat and pull out a marble. The probability of pulling out a green marble is 2/9. How many marbles are in the hat and explain? Answered by Stephen La Rocque and Penny Nom. 





Select a month at random 
20060224 

From Josh: Find the probability that the name of a month of the year,chosen at random, begins with a consonant. Answered by Penny Nom. 





A bag contains 6 red marbles,9 blue marbles,5 green marbles. 
20060224 

From Jen: A bag contains 6 red marbles,9 blue marbles,5 green marbles. You withdraw one marble,replace it,and then withdraw another marble. What is the probability that you do not pick two green marbles? Answered by Stephen La Rocque. 





A normal distribution problem 
20060215 

From Mary: In a certain normal distribution, find the mean when the standard deviation is 5 and 5.48% of the area lies to the left of 78. Answered by Penny Nom. 





A binomial distribution exercise 
20060121 

From Belinda: In a survey of 15 manufacturing firms, the number of firms that use LIFO (a lastin firstout accounting procedure for inventory) is a binomial random variable x with n=15 and p=0.2.
a) What is the probability that five or fewer firms will be found to use LIFO? Is it unlikely that more than 10 firms will be found to use LIFO? Comment. Answered by Penny Nom. 





A probability question 
20051231 

From Ling:
Question: If an integer is randomly selected from all positive 2digit integers (i.e., the integers 10, 11, 12, . . . , 99), find the probability that the integer chosen has
(a) a 4 in the tens place
(b) at least one 4
(c) no 4 in either place
Answered by Penny Nom. 





A probability question which resulted from a game of Yahtzee 
20051231 

From Robert: Could someone please assist me with this probability question which resulted from a game of Yahtzee we were playing in Melbourne, Australia on our holidays.
The object on this turn was to throw a “large straight” which is 5 numbers in sequence from 5 dice numbered 1 – 6. A player initially throws all 5 dice and then selects those dice they want to throw again for a further two more times. In this instance the player on their first throw, threw a 1,2,3,4 and 6.
Question: What is the respective probabilities of gaining a straight if they were to –
a) put back say the 6 and try and throw a 5 on the two further throws or…..
b) put back the 1 and 6 and try and throw a 1 and 5 or 5 and 6 on the two further throws bearing in mind that if one of the numbers was a 5 on the second throw they could hold that number and try for a 1 or 6 on the third throw.
I would be most appreciative if someone could assist in showing me how to calculate the probabilities particularly in the second instance (b). Answered by Penny Nom. 





Mean and average 
20051222 

From Jerry: This is just a question from a degreed engineer that has a "understanding" problem. please go to http://www.metrika.com/3medical/hemoglobinm.html
At the end of the page they talk about "mean" vrs "average" there does appear to be a difference. What is it?
Answered by Harley Weston. 





Josh and John were both exposed to the flu 
20051216 

From Dudley: Josh and John were both exposed to the flu. John has a 25% chance of getting it, while Josh has a 75% chance of getting it. What are the chances that at least one of them has the flu?
Answered by Penny Nom. 





The temperature in June 
20051212 

From Farina:
Question: Hi, I was having problem doing this problem.
Question:
Suppose the temperature during June is normally distributed with the mean= 20 degrees C and standard deviation= 3033 deg. A i the event that temperature is between 21.11 deg C. B is the event that the temperature is over 25Ged C. Event C is the temperature is below freezing point. Find the following probabilities:
A) P(A)
b) P(B)
C) P(C)
D) P(C given B)
E) P(neither A nor B)
F) find the expected number of days in June when event B will occur.
I know how to find questions AD
I am only having problem with question E and F. Can you please help me. Thank You.
Answered by Penny Nom. 





Four 25sided dice 
20051124 

From dan: Simply put, I am curious to find the likelyhood of each possibility (4100) if I were to roll 4 25sided die. It seems to start off simply, as 1, 4, 10, 20...following the inside diagonal of Pascal's triangle. But as soon as i reach the point where the sum is greater than the number of sides, Pascal's no longer seems to work. I would be greatly appreciated if I could be informed of the proper formula to find this answer, or perhaps if my theory of doing it is wrong. Answered by Andrei Volodin and Shaun Fallat. 





A standard normal probability 
20051119 

From Pat: Find the probability of Z when it lies between 1.10 and 0.36 Answered by Penny Nom. 





Seven consecutive reds in roulette 
20050904 

From Joe: I know that the odds are a little less than 50% for either black or red comming up on a spin of the roullette wheel. My question is what are the odds of red or black comming up 7 times in a row? Answered by Penny Nom. 





Probability and smoking 
20050424 

From Sean: 20% of a certain population smoke. For smokers the probability of dieing of lung cancer is ten times what it is for nonsmokers. Over all the probability of dying of lung cancer is .006. Find the probability for smokers and nonsmokers. Answered by Chris Fisher. 





Bayes Theorem 
20050403 

From wei:
In the January 11,1988,issue of the Oil&Gas Journal, R.A.Baker
describes how the Bayesian approach can be used to revise probabilities
that a prospect field will produce oil. In one case he describes,
geological assessment indicates a 25% chance the field will produce
oil. Further,there is an 80% chance that a particular well will strike
oil given that oil is present on the prospect field.
 Suppose that one well is drilled on the field and
it comes up dry. What is the probability the prospect field will
produce oil?
 If two wells come up dry, what is the probability
the field will produce oil?
 The oil company would like to keep looking as long
as the chances of finding oil are greater than 1%. How many dry wells
must be drilled before the field will be abandoned
 If the first well produces oil,what is the chance
the field will produce oil?
Answered by Andrei Volodin and Penny Nom. 





Discrimination based on gender? 
20050310 

From A student: After being rejected for employment, Kim learns that the Bellevue office has hired only two women among the last 20 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men and women. Help her address the charge of gender discrimination by finding he probability of getting two or few women when 20 people are hired, assuming that there is no discrimination based on gender. Does the resulting probability really support such a charge? Answered by Penny Nom. 





Perfecting an ideal gambling system 
20050306 

From Gaz: I am a screenwriter, currently in the fortunate position of having the development of a Screenplay funded by the South Australian Film Corporation. The (anti)hero of this screenplay is a statistician whose life is falling apart around him, thanks in part to his obsession with perfecting an "ideal" gambling system. Answered by Andrei Volodin. 





Probability 
20041204 

From A parent: Consider a 30 sided polygon. If three diagonal are selected at random, what is the PROBABILITY that they share a common endpoint? Answered by Denis Hanson. 





Select a card from the deck. 
20041202 

From Heidi: Select a card from the deck. What is the probability that this card will be red? Show the number of expected outcomes versus the number of total possible outcomes. What type of event does this represent? Answered by Penny. 





Computing confidence intervals 
20041126 

From Christie: I was given a question with N=100, sample proportion is 0.1 compute the 95% confidence interval for P? I have tried this several ways but do not know how to do without means, standard deviations, standard error of the mean? I asked my teacher and she said I have all the info I need. Can you help???? Answered by Penny Nom. 





Tennis balls and probability 
20041101 

From Jeremy: I have a hopper of tennis balls that contains 25 new tennis balls and 10 old tennis balls. In the hopper the tennis balls are mixed up randomly. If i take one ball out of the hopper and hit it and then put it back and then take another ball out of the hopper and hit it and put it back, what is the probability that i hit two new tennis balls? Also a tennis ball becomes old after being hit just once. Answered by Penny Nom. 





Pizza for Jack? 
20040916 

From Grace: Jack is playing pool with Jim for $1 a game. He has only $2 and decides to play until he goes broke or has $5, at which point he will quit and go out for a pizza with Jim(Dutch treat). Jack knows from past experience that he beats Jim 60% of the time. What is the probability that Jack will get to eat pizza? Hints: Let A be the 6x6 matrix defined by A=[aij], where aij is the probability that Jack will have $(i1)after one game is he starts with $(j1). For example, a23  .40 since there is a 40% probability that Jack will end up with $1 after a game is he starts the game with $2 (If Jack wins 605 of the time, he must lose 40% of the time). Also, for example, a52 = 0 since there is no way jack can have $4 after one game if he had $1 at the beginning of the game. Since Jack will stop if he goes broke or accumulates $5, a11 and a66 are both 1.
Let x0 = [0 0 1 0 0 0 ] transposed, which we interpret as saying that initially Jack has $2 with a probability 1. Then Ax0 will represent the porbability of each amount of money, $0$5, after one game. What is the probability that Jack will be able to eat pizza by computing Akx0 for large k and finding a limiting value. Answered by Penny Nom. 





A probability question 
20040815 

From Gary: In a law school class, the entering students averaged about 160 on the last
LSAT; the standard deviation was about 8. The historgram of the lLSAT
scores follwed the normal curve reasonable well.
Q. About what percentage of the class scored below 166?
Q. One student was 0.5 above average on the last LSAT, about what percentage
of the students had lower scores than he did? Answered by Penny Nom. 





an integer with three factors 
20040803 

From A student: What is the probability that a randomly chosen 3 digit number has exactly 3 factors Answered by Penny Nom. 





Undercapatalized small businesses 
20040626 

From Greg: Suppose that 30% of all small businesses are undercapitalized. 40% of all
undercapitalized small businesses fail and 20% of all small businesses that
are not undercapitalized fail. A small business is chosen at random. The
probability that the small business succeeds if it is undercapitalized is? Greg
Answered by Penny Nom. 





Forty balls are placed in a bag 
20040619 

From Sheila: Forty balls numbered 110 are placed in a bag and four are drawn at random. What is the probability that the first ball drawn is between 110 (inclusive) the second is between 1120, the third is between 2130 and the last is between 3140? Answered by Penny Nom. 





Three dice 
20040510 

From A student: If one has 3, 6 sided dice what is the probability of the numbers that are rolled to total 4 through 10 inclusively?
Subsequent to this, what is the probability to do this consecutively...say 3 times? Answered by Peny Nom. 





A probability density function 
20040414 

From A student: The label on a bottle of liquid detergent shows contents to be 12 ounces per bottle. The production operation fills the bottle uniformly according to the following probability density function:
f(x) = 8 for 11.975 <= x <= 12.10
and
f(x) = 0 elsewhere
a. What is the probability that a bottle will be filled with 12.02 or more ounces?
b. What is the probability that a bottle will be filled between 12 and 12.05 ounces?
c. Quality control accepts production that is within .002 ounces of number of ounces shown on the container label. What is the probability that a bottle of this liquid detergent will fail to meet the quality control standard? Answered by Penny Nom. 





Replacement times for TV sets? 
20040331 

From Barb: Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years. Estimate the probability that for 250 randomly selected TV sets, at least 15 of them have replacement times greater than 10.0 years.e Answered by Andrei Volodin and Penny Nom. 





Four marbles on a box 
20040322 

From Karyn: Suppose 2 solid color marbles and 2 striped marbles are placed in a box. All are the same size. If one marble is randomly drawn from the box and replaced, then a second marble is randomly drawn, what is the probability that the marble drawn both times will be striped?
I know there is a simple formula for working this out but I can't remember how.
Answered by Penny Nom. 





Selecting balls from a golf bag 
20040221 

From A student: There are 5 white and 5 yellow balls in a golf bag. Two are selected randomly, and simultaneously. What is the probability that the first one or the second one will be white? Answered by Penny Nom. 





Probabilities and olivies 
20040214 

From Annetta: A bowl contains five green olives and eight black ones. Wilma sticks a fork into a bowl and brings out two olives. What is the probability that she gets one green and one black olive? Answered by Harley Weston. 





A game with some strings 
20040122 

From Trudy: A boy holds 6 pieces of strings in his hands with the ends protruding above and below. The top ends are tied together in pairs and then the lower ends are tied together in pairs. What is the probabilty that the pieces of string are all joined in one loop?
What is the probability of obtaining two loops?
Can you generalise this to solve the problem for 2n blades of grass? Answered by Andrei Volodin and Penny Nom. 





Unusual occurances 
20040108 

From Martin: My wife and I have a question about the probability of something that happened to us a few years ago. So far, no one has been able to give me even an approximate answer. On my 32nd birthday, my wife and I went out to eat at local Japanese hibachi style restaurant. At the restaurant, couples/families are sat together around the hibachi where the cook performs a show. There was a fifteen minute or so wait, so my wife and I sat in the lounge waiting for our name to be called. When they called our names for the reservation, this is what happened. The first group called was the Martin family. Then they called the Francis family. We were the next family to be called, the Ashton family. My full name is Martin Francis Ashton! I think the odds of that happening to someone are very unlikely, but it did, and there is more. Next, we were all sat at the same table in that order, "Martin" family, "Francis" family, then us, the "Ashton" family. Again, it formed my full name! Answered by Penny Nom. 





Binomial distribution 
20031217 

From Lesley: my daughter is having difficulty with the following formula
P(X=x) = ( n over x) px (1p) nx
The teacher has given them the formula but not taught them how to apply it or understand it. Answered by Penny Nom. 





Unmatched socks 
20031117 

From Shannon:
i have 6 pairs of socks lying unmatched in my dresser drawer. Each pair is a differnt color (brown, black, red, yellow, green, purple) When i wake up in the morning, I randomly grab 2 of the loose socks and put them on without looking.
If two socks are randomly selected from the drawer, what is the probability that they match?
Answered by Andrei Volodin. 





Diagonals in an octagon 
20031113 

From Glenn: Question 1. What is the probability of choosing the longest diagonal in an octagon? Question 2. Probability of choosing the shortest? Answered by Andrei Volodin and Penny Nom. 





12 cookies 
20031029 

From Joel: there are 12 chocolate, sugar and cinnamon cookies. the probability of choosing a chocolate cookie is 1/3. the probability of choosing a sugar cookie is 1/4 what is the probability of choosing a cinnamon cookie Answered by Penny Nom. 





The effectiveness of a drug 
20030422 

From A student: A certain drug is found to be effective 80% of the time. Find the probability of successful treatment in two out of four cases. Answered by Andrei Volodin. 





A royal flush 
20030324 

From Vikki:
A poker hand consists of 5 cards selected randomly from an ordinary deck of cards: find the probability of a ROYAL FLUSH : the 10 , jack, queen,king and ace of the same suit. I was thinking somewhere along the lines of: *the number of ways to get the suit is 4C1 *the number of ways to get a 10 out of the 13 cards etc.... ...but Im not sure I am going about this the right way, could you help? Answered by Andrei Volodin. 





Would it be worth paying $20K for 4 chances... 
20030113 

From Steve:
If I've got 4 chances to to achieve X goal, and in each chance that I have I've got a 65% chance of achieving this goal, what is my overall probablity of achieving this goal? Also, what would it be after each of my 4 chances (i.e., for my 2nd chance, would it be (.65 * (.65*.65)? I've forgotten some basic probablity theories, and would appreciate any help on this. With the probablities above, would it be worth paying $20K for 4 chances to achieve the goal or $8.5K for only 1 chance to acheive the goal? (at 65% probability) Answered by Andrei Volodin. 





A Normal probability problem 
20021203 

From A student: The height of married men is approximately normal with mean 70 and standard deviation 3. The height of married women is approximately normal with mean 65 and standard deviation 2.5. What is the probability that a random married woman is taller than a random married man? Answered by Andrei Volodin. 





A coin is tossed 11 times 
20021031 

From A student: There are 2 people that are playing a game in which a coin is tossed 11 times. The first player gets a point for a toss of heads. The 2nd player gets a point for a toss of tails. whoever gets 6 points wins. Suppose that so far the first player has 2 points and the second player has 4 points. What is the probability that the first player wins the game? Answered by Andrei Volodin and Penny Nom. 





Probability 
20020816 

From Chris:
There are two possible outcomes for a random event, A and B. The probability of A being the outcome is 63%, and B 37%. What is the likelihood that B will be chosen twice, consecutively? Three times, ten? Answered by Andrei Volodin. 





A probability problem 
20020712 

From Yvonne: What is the probability of 38 people choosing the same five options, given a choice of 15? Perhaps you could just give me the formula with an explanation. I am an English teacher doing educctional research, but am stuck because I don't have the math experience to help me. Answered by Andrei Volodin. 





Drawing cards 
20020611 

From Ed: What is the probability of drawing without replacement from a standard deck of 52 cards the following 5 card hand ...... the ace of spades, 2 tens and 2 face cards Solution 1: ^{1}/_{52} x ^{4}/_{51} x ^{3}/_{50} x ^{12}/_{49} x ^{11}/_{48} Solution 2: Using Combination theory ..... (1C1 x 4C2 x 12C2) divided by (52C5) Can you help us understand which answer is correct and why the other is not? Answered by Penny Nom. 





Blood donations 
20020523 

From Fiza: One particular high school encourages students to donate blood. the high school gym is set up for purpose. the distribution of blood type in north america is as follows.
Type O:44% Type B:10% Type A:42% Type AB:4% (a) what is the probability that the first two people in the line up have the same type of blood? ANSWER: I donn't know how many people are in the line. so how can I answer this question. (b) what us the probability thar none of the first five people in the line up have type AB blood? Answered by Andrei Volodin. 





Telephone banking 
20020522 

From Fiza: To use telephone banking to pay bills, the customer has to enter the last three digits of each bill. the numbers 0 to 9 can be used. if the number happened to be the same on more tan one bill, the customer has to enter the first three digits as well. (a) what is the probability that a person has 2 bills to register with the same last three digits? ANSWER:P(2 bills to register)=1/10P3 1/(10!/7!), 1/(10*9*8)=.001389 (b) what is the probability that a person with 10 bills to register has at least 2 bills with the same last three digits? ANSWER:P=1/(10*10*10) =0.001 Answered by Andrei Volodin. 





Probability and investment 
20020519 

From Bally: Investors do not invest all their money in the investment predicted to be the best beuause it is too risky. an investor holds shares in three independent cmpanies. company A, Company B, compnay C. an analyst predicts the probability of profit increases for each company as follows. Company A:0.70 Compamy B:0.50 Compnay C:0.65 (a) If the analyst's predictions are true, what is the probability that all three comapanies show a profit incresse?
ANSWER: I try using vin diagram but it did'nt work, I dont know any other ways to solve this question (b) if the analyst's predictions are true, what is the probability that at least one comany shows a profit increase? Answered by Andrei Volodin. 





Conditional probability 
20020519 

From Manny: In a certain school, it is known that 80% of the students use the internet for school projects, 60% use email on a regular basis, and 90% use the internet for school projects or for email on a regular basis. a student from this school is selected at random Determine thge probability that the student used email, given that the student used the internet for school projects. ANS: how can i solve this question by useing the vin diaagram Answered by Andrei Volodin. 





On which assignment did I do better 
20020517 

From Denise: I have 2 writing assignments in class. The first assignment, which had a mean of 10 and a standard deviation of 2, I got a score of 12. The second assignment had a mean of 18 and an s.d. of 3, I got a 21. I need to know which assignment did I do better, relative to my classmates? Answered by Andrei Volodin. 





A game of dice 
20020513 

From Mika: To play a game a dice is rolled to see who plays first. four players are going to play the game. what is the probability that at least two people roll the same number? ANSWER: P(least 2 people roll the same #)=number of player/total outcome P = 4!/4C2 = 24/4C2 = 4 the answer is 40% Answered by Andrei Volodin. 





An award ceremony 
20020513 

From Mika: Five students are equally qualifide their school at an award ceremony. two students will be randomly chosen to go to the ceremony.
(a) if Tony is one of the five student, what is the probability that he will be chosen? Ans: 2/5C2=0.2 which is 20% (b)Tony's friend, Allecia, who was also eligible to go, has been chosen. what is the Tony's probability of being chosen after he learns that allecica is going: Ans: 1/5C1=0.2 I think the answes are wrong please help me with these questions Answered by Andrei Volodin. 





Forming a committee 
20020506 

From Navi: A committee is to be formed to investigate what activites teenagers have available in small communities. the committee is to have 7 members, chosen randomly form interested community members. there are 10 parents, 5 teenagers, and 4 adult without children who have all expressed an interest in serving on the committee. what is the probability that the adults without children are all on the committee? Answered by Andrei Volodin and Penny Nom. 





Oven lights 
20020506 

From Manny: Q.A manufacturer of stoves has to buy oven lights from from two diffrent companies because one company alone cannot meet its demand. the manufacturer purchases 60% of the oven lighs from comany A and the rest form Company B. Past experiecnce shown that 1% of Company A's oven are defective oven and 2.5% of Company B's oven light are defective. Determine the probability that a defective oven light is supplied by company A. Answered by Andrei Volodin. 





A probability tree 
20020504 

From A student: Karl and Naomi roll three dice. Karl gives $10 to Naomi if the number 5 turns up once, twice or three times. Naomi gives Karl $3 in all other cases. A) construct the probability tree for this situation.
B) Does Karl have an advantage in this game? Justify your answer. My problem is I am unfamiliar on how to draw this probability tree and seem to be having a lot of difficulties, when you have a chance please answer this math problem and get back to me with the results. Answered by Penny Nom. 





All four eights in three consecutive hands 
20020401 

From Blair: What are the odds against the same person holding all four eights in three consecutive hands. Answered by Brian Alspach. 





A lottery question 
20020325 

From Noel: I want to take all numbers in a Lotto game from 1 to 45 and ditribute them between 9 boxes each containing 5 numbers. Each number is used only once.  What is the probability that I derive the correct combination of 5 numbers in the draw?
 What is the probability if I take a systems game and now distribute 9 numbers into each of 5 boxes? Once again, the numbers are used only once.
 Can you explain what formulae are used and how the answer is derived? Is this a distribution or combination problem? Or is it a combination of both distribution and combination?
Answered by Andrei Volodin and Penny Nom. 





A probability problem 
20020323 

From Kate: If I have a spinner and then spinner has the numbers 1,2,3,4 on it and it is spun 3 times, what is the probability that the spinner will stop on 4,3,and 1 ? In that order? Answered by Leeanne Boehm. 





Rolling 5 sevens before rolling a six or an eight 
20020120 

From Tony: When rolling 2 dice, what is the probability of rolling 5 sevens before rolling a six or an eight? Answered by Andrei Volodin and Penny Nom. 





Children and probability 
20020116 

From Bill: If a family has four children, what is the probability that all 4 are the same sex? Answered by Vanrei Volodin. 





The probability that the area of a triangle is smaller that 1/8 
20011221 

From Hoda: Given unit square pick two points on adjacent sides of the square , what is the probability that the area of the resulting triangle is smaller that 1/8? I tried to tackle the problem by first sketching a square with the four vertices at (0,0), (1,1), (0,1) and (1,1). The answer seems to be the area under the curve y=0.25/x between 1 and 0, but how can you integrate such a function when ln0 is undefined? any help would be highly appreciated. Answered by Andrei Volodin. 





Cinderella clothes 
20011211 

From A student: If cinderella clothes, inc. has determined that 0.5% of all incoming phone calls involve complaints, what is the probability that in 200 incoming calls there are more than one complaint? Answered by Andrei Volodin. 





A health club 
20011125 

From Maria: A health club with a membership of 650 people operates a running track and an indoor swimming pool. A survey of the membership indicates that 68% use the running track, 44% use the swimming pool, and 8% use neither. If a member is chosen at random, what is the prbability that the member uses: a) Both the track and the pool? b) Only the track? Answered by Penny Nom. 





Is the tree a pine tree? 
20011027 

From Kate: Suppose Stock Brokers tell the truth 2/5 of the time, and 1/3 of the trees in a given forest are Pine. If 4 Stock Brokers say that a certain tree in that forest is Pine, what is the probability that the tree is indeed a Pine tree? Answered by Penny Nom. 





A bag with 3 red marbles and 
20010927 

From Mike: In a bag, there are 3 red marbles and "B" blue marbles. Two marbles are randomly selected from the bag without replacement. The probability that the two marbles are the same color is 0.5. Calculate the sum of all possible values of B. Answered by Claude Tardif. 





Rolling two dice 
20010910 

From Owen: This probability question has been bugging me for a while. Two ordinary dice are rolled. If it is known that one shows a 5, what is the probability that they total 8? I have two different but (seemingly) correct solutions. Answered by Andrei Volodin. 





72 cards 
20010903 

From A student: What would be the probability of dealing a deck of 72 cards out in the exact orderly sequence that they were in when they were packaged after they have been throughly shuffled? Answered by Andrei Volodin. 





Mutually exclusive 
20010605 

From Marje: What does the mathmatical term "mutually exclusive" mean. Pleas diagram if possible. Answered by Penny Nom. 





SPRT 
20010524 

From A researcher: I have a medicalpharmaceutical study that says: SPRT (something to do with Secuential and Truncated). Do You know what it means S.P.R.T. and what it is? Answered by Ejaz Ahmed and Penny Nom. 





Probabilities and dice. 
20010504 

From Carmen: Hi! My name is Carmen! I am a member of a grade 5 class in Edmonton, AB. We were talking about probability in math, and I was wanted to know what the probability (odds) of rolling two sixes would be rolling two dice? If it is not to diffucult could you tell me what the probability (odds) of rolling any number with two dice were? Answered by Andrei Volodin and Penny Nom. 





Choosing a car 
20010428 

From Ashley: THE CAR DEALERSHIP IN TOWN OFFERS 32 DIFFERENT MODELS OF VIHICLES.EACH MODEL HAS A CHOICE OF EIGHT INTERIOR COLORS,EIGHT EXTERIOR COLORS,AND ALSO THE OPTION OF AUTOMATIC OR MANUAL TRANSMISSION. HOW MANY COMBINATIONS ARE POSSIBLE? Answered by Penny Nom and Andrei Volodin. 





A lemon and a recall 
20010425 

From Katie: A Man has two cars, a recall and a lemon. The probability that the recall starts is 10%. The proabability that the lemon will start is 5%. What is the proabability that both cars will start? Answered by Andrei Volodin. 





Expected value 
20010424 

From Cindy: A game consists of rolling a single fair die. If a number great than 4 is rolled you win the number of dollars showing on the die. If any other number is rolled, you receive $1.00. What is the expected value of this game? Answered by Andrei Volodin. 





A few problems 
20010422 

From Carol: Hello I am a College student trying get through my elmentry concepts class. I am also working with the middle and elementry school student with their work. I was given a few problems to work on and i am having a hard time explaining them to students. DO you think you can help with a coupld of these questions! Answered by Penny Nom. 





Leukemia 
20010415 

From Don: Assume: Leukemia occurs at an incidence of 1 in 10,000. Benzene is a known carcinogen which causes Leukemia and has been found in toxic levels in the homes of a community of 1200 people. Question: How many cases of Leukemia would be necessary to reject the null hypothesis. That is, to suggest that statistically, the cases are more likely due to benzene exposure rather than chance. Answered by Chris Fisher and Penny Nom. 





Mistie, Tammy, and Jennifer 
20010327 

From Renee: Mistie, Tammy, and Jennifer audition for parts in a bigbudget remake of Bedtime for Bonzo. On the basis of their past experience and the caliber of competition they face, Mistie has a 40% chance of being hired, Tammy has a 50% chance, and Jennifer has a 30% chance. If exactly two of the three are cast, what is the probability that Mistie was rejected? Answered by Andrei Volodin. 





Probability and a three digit number 
20010315 

From Glenn: A THREE DIGIT NUMBER IS SELECTED AT RANDOM. WHAT IS THE PROBABILITY THAT NON OF THE THREE DIGITS ARE PRIME. Answered by Harley Weston. 





Spins of a roulette wheel 
20010302 

From Bob: Here's a problem I'm working on myself.....If you look at six consecutive spins of a roulette wheel, how many combinations of red and black are possible? I.E. BRRBRB, BBBBBR, BBRRRB......ETC..... Answered by Claude Tardif. 





Winning percentages 
20010221 

From Mike: TEAM A WINS 55% OF GAMES PLAYED TEAM B WINS 40% OF GAMES PLAYED AGAINST THE SAME OPPONENTS WHAT WINNING PERCENTAGE SHOULD BE EXPECTED WHEN TEAM A PLAYS TEAM B (NEUTRAL SITE)? Answered by Harley Weston. 





Lucky dip 
20010209 

From Andrew: I buy 8 lucky dip (random number) panels, each panel has 6 numbers chosen at random from 49. I never seem to cover more than 32 different numbers on average, over the total 48 numbers chosen, which seems low? How can I calculate the probability of 32 different numbers or 33 diferent numbers? Answered by Claude Tardif. 





The odds of winning 
20010209 

From Anna: The odds of winning in a game are 3 out of 10. How many times would one have to play the game in order to be sure they would win? Answered by Leeanne Boehm. 





Conditional probabiity 
20010122 

From Wallace Yang: A pair of sixsided fair dice is thrown. Find the probability that the sum is 10 or greater if it is given that a 5 appears on at least one of the dice. Answered by Penny Nom and Claude Tardif. 





A 1 from 35 lottery 
20010111 

From Jamie: A number is randomly drawn from an urn containing 35 balls numbered 00 to 34. How to win Division 1 Match the number drawn Division 2 Match the last digit of the number drawn Calculation of probabilities for this lottery:... Answered by Claude Tardif and Penny Nom. 





Banana yogurt 
20001103 

From James: A grocery store has 100 cartons of banana yogurt in stock.Each carton contains 12 cup of banana yogurts.The probability that a cup has fewer than 20 banana chunks in it is 10 %. So,What is the probability that between 15 and 25 (inclusive) cartons out of the 100 cartons have exactly 3 cups with fewer than 20 banana chunks? Answered by Harley Weston. 





False Positives 
20001029 

From James: A rare disease infected 1 in 1000 people in the population. A test for the disease is accurate 99% of the time when given to an infected person and also when given to a heathy person.  Fill out a twotier tree diagram and find the probability of the false positive(i.e the conditional probabily of being healty even when tested postive by the test) Comment on the result?
 ...
Answered by Penny Nom. 





Independent tests 
20001007 

From A student: If the falsepositive rate of each test in a battery of tests is 0.05, how many independent tests can be included in the battery if we want the probability of obtaining at least one falsepositive result to be at most 0.2? Answered by Harley Weston. 





Probability of a square 
20000918 

From Nick: What is the probability that four different points chosen at random from the fifteen equallyspaced points shown are the vertices of a square? I need to have my answer expressed as a common fraction. Help! I don't know how to write it. . . . . . . . . . . . . . . . Answered by Penny Nom. 





Review problems 
20000918 

From Dee: A card is selected from an ordinary deck of cards. What is the probability of. . . selecting 2 aces in a row? If you toss two dice, what would be your probability of the following? . . . Answered by Penny Nom. 





Odds and combinations 
20000510 

From Lucy: If the odds are 1/15 of winning, what is the probability? if c 5! 3! How does it equal 10? Answered by Harley Weston. 





Probability and odds 
20000505 

From Leah: The chances of rain on friday, saturday, and sunday are 20%, 30%, and 50% respectively. what are the odds it will rain all three days? Answered by Harley Weston. 





An expected value 
20000424 

From Carl Pride: Suppose that in a statistics class of size 23, each student has a probability of passing of 73 percent. sample: What is the expected number of students who will pass?? Answered by Harley Weston. 





A quantitative methods course 
20000319 

From Mark Haberman: Question: Last semester, the grade distribution in a quantitative methods course had the following distribution: 10% A, 25% B, 35% C, 10% D, and 15% W (withdrew).  If this grade distribution does not change this semester, what is the probability that a randomly selected student will make at least a D?
 If this grade distribution does not change this semester, what is the probability that a randomly selected student will fail the course?
 If this grade distribution does not change this semester, what is the probability that a randomly selected student who finished that course (did not withdraw) made a grade of D or better?
Answered by Harley Weston. 





Probability, graph theory and VLSI testing 
20000127 

From Valentin Muresan: I am postgraduate student of Dublin City University, Ireland, in the field of VLSI Testing. I am currently working on some heuristics and I need a probability formula. I want to get an expert's point of view in my matter. Say there is an initial list of so called tests: T1, T2, T3, ..., Tn Every test element Ti of the above list has a list of compatibility (incompatibility), which includes all the elements (tests) from the initial list, the Ti test is compatible (incompatible) with. For example, say the initial list is: {T1, T2, T3, T4, T5, T6, T7, T8, T9, T10} and the compatibility lists of these elements (tests) are: . . . Answered by Denis Hanson. 





A probability experiment 
20000105 

From Vanessa: Duels in the town of Discretion are rarely fatal. There, each contestant comes at a random moment between 5 a.m. and 6 a.m. on the appointed day and leaves exactly 5 minutes later, honor served, unless his opponent arrives within the time interval and then they fight. What fraction of duels lead to violence? There must be a minimum number of 100 trials and things like graphing calculator, dice, spinners, and whatever are allowed. Answered by Harley Weston. 





Parachute Problem 
19991228 

From Stephanie Zinsli: A parachutist jumps from an airplane and lands in a square field that is 2 kilometers on each side. In each corner of the field there is a large tree. The parachutist's ropes will get tangled in the tree if she lands within 1/11 kilometer of its trunk. What is the probability that she will land in the field without getting caught in a tree? Answered by Penny Nom. 





.400 in Baseball 
19991215 

From Nieve Nielson: I have several questions to ask about the probability of getting a .400 in baseball:  What is the probability of a baseball player hitting a .400 in one game, considering that the hitter is up to bat four times?
 What is the probability of a baseball player hitting a .400 in a season, considering that there are 100 games in a season? With the first two questions in mind:
 Considering that baseball has been around for about 100 years, about how many people should hit .400 inthat time?
Answered by Chris Fisher. 





A matching quiz 
19991120 

From William J. Ricciardi: I gave a matching quiz the other day and one of my students got all 9 incorrect. That got me thinking......What is the probability that someone could get all 9 questions incorrect? Answered by Peny Nom. 





A Multiple Choice Test 
19990831 

From Cintra Ramnarine: I have ten questions. There are two multiple choice answers to each question. What are the chances of answering all questions correctly. Answered by Harley Weston. 





The birthday problem 
19990419 

From Gordon Cooke: How do I explain the rapid rise in the probability that at least two people in a group of n have the same birthday. We have derived the formula for p(n) and have graphed it and have seen how the results are counterintuitive. At around n=23 p(n)=.5 and at n=50 p(n) is very close to 1. It does not help to simplify the problem (eg use months instead of days) because then our intuition does correspond more closely to reality. Is there some way we can see how the probabiltiy of a "collision" increases with n? It makes me think of data storage problems and hash tables in computer science. Answered by Harley Weston. 





Instant Winner 
19990407 

From FSSTAN: The probabilities of being an "instant winner" of $25 or $50 in a lottery are 1/600 and 1/1200, respectively. The mathematical expectation of being an "instant winner" of $25 or $50 is? Answered by Jack LeSage and Penny Nom. 





Probability and Statistics 
19990325 

From Karrie Waller: Hi my name is Karrie and I am an elementary ed. student at Florida State University in Tallahassee, Florida. I am doing a report on how children learn probability and statistics. I am having trouble locating information that will tell me specifically how students learn. I am wondering if you can answer this question for me or direct me in the right direction. Answered by Jack LeSage. 





Three keys 
19981126 

From Karen Chan: A man has a bunch of three keys, only one of which fits the lock of his front door. When he comes home in the dark he tries the keys at random until he finds the one fits. Find the probability that in a week of five nights, he tries the right key first on at least one night. Answered by Penny Nom. 





Probability 
19980917 

From Chris: Six marbles are placed in one of three boxes. What is the probability that each box contains two marbles? What is the formula used? Answered by Penny Nom and Chris Fisher. 





Snake Eyes 
19980720 

Would you please advise me what the probability is of rolling snake eyes on a pair of dice is? My recollection is 1 out of 6 multiplied by 1 out of 6 = 1 out of 36 is this correct? Answered by Jack LeSage and Penny Nom. 





The Birthday Problem 
19980612 

From Josh Skolnick: if you are at a party what is the least amount of people that have to be there to have at least a 50% chance of having 2 people with the same birthday? and how do you get the answer thank you in advance josh Answered by Harley Weston. 





Rolling a seven 
19980611 

From Bruce Thompson: What is the probablity of rolling two dice and it coming out as seven? a) 1/6 b) 1/36 please give me the correct awnser and explain please. Answered by Harley Weston. 





15 films 
19991109 

From Hebert: Un touriste revient de vacnces avec 15 films:  2 films de photos d 'Italie
 8 films de photos de Grèce
 5 films de photos de Turquie.
Aucune marque distinctive ne permet d'identifier les films. Pour des raisons financières le touriste ne fait développer à son retour que 11 de ces 15 films qu'il choisit au hasard.NB : on donnera les résultats sous forme décimale approchée à 104 près.  Combien y a t il de choix différents possibles de 11 films parmi les 15 ?
 Quelle est la probabilité que , parmi les 11 films développés, il y ait:
 ...
Answered by Claude Tardif. 

