Our question is:
A pair of six-sided 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.
I see two methods to approach this; yielding different answers.
Both arguments seem logical. Please tell us how you see it, and indicate the flaw in the logic of the other one, or may be both.
Thank you for your help.
Wallace Yang (student) and Mr. McMaster
They are both logical and both yield correct answers, but correct answers to two different questions. One question is
For the problem you have stated
These two problems are related to the following apparent paradox: Suppose that I throw the two dice where I can see them but you can't, and I tell you (honestly) that at least one 5 appears. Then you have a probability of 3/11 of having a sum of at least 10. If I had told you instead that a 5 appears on the red die, this probability climbs to 1/3, and similarly, if I were to tell you instead that a 5 appears on the blue die, this probability would also be 1/3.
Now the problem is this: If it is true that at least one five appears, then it must be true that five appears on the red die or five appears on the blue die. So, instead of telling you "There is at least one five" (leading you to conclude that the probability is 3/11), I could always tell you one of "there is a 5 on the red dice" or "there is a 5 on the blue dice", (leading you to conclude you are in one of two situations, each of which yields to a probability of 1/3).Cheers,
Penny and Claude