







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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 

