







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. 





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. 





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 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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 

