a) I have a pair of fair n-sided dice. The probability when both are rolled that their results differ by two is the same as that the sum will be 5 or less. Find n.

b) I have two dice, one with n sides and the other with m sides. When they are rolled the probability they are equal is the same as that they sum to 13 or higher. Find n and m.

c) I have a trio of n-sided dice. When I roll them all the probability that the dice all show different numbers is greater than when they sum 15 or less but less than when they sum 16 or less. Find n.

Note: "x sided dice" are numbered with consecutive integers from 1 to x.

This is not meant to be a conditional probability.  A slight wording change was made to clarify the problem when it was in the queue.  Apparently the problem became less clear.

Here is the problem in part c) written more explicitly:

We have three events:
I the sum is 15 or less,
II all the dice show different numbers,
III the sum is 16 or less.

Find n such that P(I)<P(II)<P(III)

(Hope that helps)

Posted by Jer on 2006-12-01 10:56:36