







Drawing a counter from 2 bags 
20200521 

From Sephy: Question 4: Two bags, 1 and 2, each contain equal size counters.
Bag 1 contains a pink counter, yellow counter and white counter.
Bag 2 contains counters labelled 1, 4, 5 and 7.
A counter is drawn at random from bag 1
and a counter is drawn at random from bag 2.
If the counter from bag 1 is pink, the number on the
counter from bag 2 is increased by 1
If the counter from bag 1 is yellow, the number on the
counter from bag 2 is decreased by 5
If the counter from bag 1 is white, the number is halved.
Find the probability of scoring a number below 3 Answered by Penny Nom. 





Soccer fans and cricket fans 
20180506 

From Chibo: In a survey of 60 sport fans, 45 enjoy soccer, 35 enjoy cricket and 10 do not enjoy either soccer or cricket, but some other sports.What percentage of sports fans enjoys both soccer and cricket? Answered by Penny Nom. 





The modulus of a complex number 
20160729 

From Cheyenne: There's a question on my Summer Assignment I cant figure out. Here it is:
Find the absolute Value of the complex number. 5i
Please help? Answered by Penny Nom. 





How many students have neither brown hair or hazel eyes? 
20130120 

From Julie: There are 28 students in a class. 15 have brown hair, 17 have hazel eyes, and 10 have both. How many students have neither brown hair or hazel eyes? 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. 





An equilateral triangle and some circles 
20120110 

From tushar: draw an equilateral triangle with side 6cm.draw 3circles with radii 3cm on each angular point of triangle.draw common tangent on each of two circles 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. 





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. 





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. 





How many people in total came to the museum that day? 
20100305 

From simon: 1354 people attended exhibition A and 1427 people attended exhibition B. 79% of people attended both exhibitions. How many people in total came to the museum that day Answered by Penny Nom. 





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. 





Ranking 6 players from 49 
20090324 

From liz: My daughter is having problems with this question,
if you had to match 6 players in the correct order for most popular outfielder from a pool of professional players numbered 1 through 49 , how many possibilities are there? Answered by Penny Nom. 





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. 





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. 





An Euler diagram and a logic argument 
20080918 

From Regina: Use a Euler diagram to determine whether the following argument is valid or invalid.
No wizard can yodel
All lizards can yodel
No wizard is a lizard Answered by Penny Nom. 





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. 





Two forces acting on a body 
20080621 

From Rita: Before answering the question below, what exactly is, in basic words, resultant force?
QUESTION:
Two forces of 50 and 68 pounds act on a body to produce a resultant force of 70 pounds.
Find, to the nearest 10 minutes or nearest tenth of a degree, the angle formed between the resultant force and the smaller force. Answered by Harley Weston. 





All wiffs are miffs and all miffs are kiffs. 
20080608 

From Allison: All wiffs are miffs. all miffs are kiffs. There are 25 wiffs. There are 76 kiffs. 33 kiffs are not miffs. How many miffs are not wiffs? Answered by Penny Nom. 





Drawing blocks from a box 
20080211 

From Inez: A box contains 3 red blocks and 1 green block. A block is chosen without looking and not put back. Then another block is chosen. What are the possible outcomes? Answered by Penny Nom. 





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. 





Forces on an inclined plane 
20080110 

From Ron: A body that weighs 540lbs is caused to slide up an inclined plane with a uniform velocity by a force that acts parallel to the plane. For each foot of horizontal distance, there is a vertical rise of 2in. If the coefficient of sliding friction is 0.16, what force is required to move the body? Answered by Stephen La Rocque. 





A thanksgiving day problem 
20071117 

From svetik: On Thanksgiving Day, a group of nutty professors dressed up as "turkeys" and participated in a local fundraising event. The event consisted of three types of races: the sprint, the relay, and the hurdles. One more “turkey” takes part in the hurdles only than the sprint only. The same number take part in the sprint and the hurdles as take part in the relay and the hurdles. Eleven of the “turkeys” taking some part in these three races do not do the relay. Five “turkeys” take part in the sprint and the relay and three enter all three races. There are four teams of four “turkeys” in the relay. And, one more “turkey” is running in both the relay and the sprint than in the hurdles only.
“Turkey” Coe turned and said to “Turkey” Kim, “How many ‘turkeys’ were taking some part in any of the three races?” The nuttiest math professor, “Turkey” Young, said “There were ________ ‘turkeys’ taking part in any of the three races.”
Fill in the blank!!! 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. 





Choosing a bicycle 
20070328 

From Jackie: A specific brand of bike comes in two frames, for males or females. Each frame comes in a choice of two colors, red and blue, and with a choice of three seats, soft, medium, and hard.
a) Use the counting principle to determine the number of different arrangements of bicycles that are possible.
b) Construct a tree diagram illustrating all the different arrangements of bicycles that are possible. c) List the sample space. Answered by Penny Nom. 





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. 





Brown hair and hazel eyes 
20050918 

From Julee: There are 28 students in a class. 15 have brown hair, 17 have hazel eyes, and 10 have both. How many students have neither brown hair or hazel eyes? 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. 





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 problem with sets 
20040120 

From Jason:
Given that the universal set S is the set of all sports fans, and
F={xx is a football fan}
B={xx is a basketball fan}
H={xx is a hockey fan}
a)Describe (F^B)' (f intersect b)' in words
b)Draw a Venn Diagram and shade the region that represents the set of football fans or both basketball and hockey fans.
Answered by Penny Nom. 





I have three circles... 
20030130 

From Tony: I HAVE THREE CIRCLE THAT IS CIRCLE TOGETHER: IN CIRCLE A, THE NUMBERS ARE: 11 I KNOW IS IN CIRCLE A, BUT I HAVE THE: 5 THAT IN A AND C, I HAVE THE 2 IN THE CIRCLE C AND B AND AND A, THE CIRCLE C I KNOW THAT 10 IS IN THE CIRCLE THE 4 IN CIRCLE A: AND B: IN CIRCLE B, I KNOW NUMBER 13 IS IN CIRCLE B; BUT I HAVE THE 3 IN CIRCLE B AND C AND I HAVE THE 2 IN CIRCLE B AND C AND A ,THE 4 IN CIRCLE B AND A. HOW DO I FIND THE SUM IN CIRCLE C AND IN B IN BOTH CIRCLE A AND B AND B AND C NOT IN CIRCLE B, AND NOT CIRCLE C. Answered by Penny Nom. 





Tree diagrams 
20021012 

From Denean:
 For lunch, students can choose juice or milk; hamburger or pizza; and a banana or apple. How many lunch combinations can the students make?
 In an experiment, Monty can use paper towels or cloth. He can choose red, green, or yellow food coloring. How many combinations are there?
Answered by Penny Nom. 





Baseball, basketball and football 
20021008 

From Debbie: The school newspaper is interviewing 6th grade students to see what sports they follow regularly on TV. Of the 70 students interviewed; 40 enjoyed basketball; 40 enjoyed baseball; 40 enjoyed football; 20 enjoyed basketball and football; 22 enjoyed baseball and basketball; 27 enjoyed football and baseball; and 12 enjoyed all three sports. How many students out of the 70 interviewed didn't follow any one of the three sports? Answered by Leeanne Boehm, Penny Nom and Walter Whiteley. 





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. 





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. 





Applied geometry 
20011102 

From Jenny: Where can I find some handson activities for my Applied Geometry classes? I want to do more activities with them that allow us to get out of the classroom. However, I want to use activities that use only inexpensive equipment because I usually buy the equipment myself. Answered by Walter Whiteley. 





Genealogy 
20010322 

From Brian: In considering tracing genealogy the problem of a large and growing number of direct (grandparent) ancestors arose. Since the number of grandparents in any given generation doubles, for a person born in 2000 and assuming 25 year generations, in the year 1000 that person would have over one trillion direct ancestors in that year alone. Since estimates I have read place the total world population in 1000 at 250300 million, the one trillion figure cannot be correct. I must be missing something in my calculations. Can you help provide the answer? While I am unlikely to be able to trace back to 1000, there is reason to believe 1250 is possible. Even in that year there would exist over one billion direct ancestors. That is certainly rather daunting and unlikely to be achieved if correct. Answered by Penny Nom. 





Derfs, Enajs and Sivads 
20010107 

From John and Norman: All Derfs are Enajs. Onethird of all Enajs are Derfs. Half of all Sivads are Enajs. One Sivad is a Derf. Eight Sivads are Enajs. The number of Enajs is 90. How many Enajs are neither Derf nor Sivad? Answered by Penny Nom. 





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. 





100% on two tests 
20000201 

From Craig and Chelsea Bruzzone: A class of 35 students took a math test and a science test. 12 students got 100% on the math test. 9 students got 100% on the science test. There were 19 students who made less than 100% on both tests. How many students made 100% on both tests? Answered by Penny Nom. 





Diagramming Powers 
19971015 

From David Fill: I am a teacher in Massachusettes. We have been diagramming numbers such as two to the third (a 3D cube). One of my students asked me how you would diagram two to the fourth. I have searched through all of my teachers books and cannot seem to find the answer to this question. Is there a way to diagram this? If there is, how would you do this? Your help would be greatly appreciated. Answered by Penny Nom. 





Diagonals in a polygon 
19960618 

From Steven: How many diagonals are there in a polygon? Answered by Denis Hanson. 

