1995 AJHSME Problems/Problem 20
Problem
Diana and Apollo each roll a standard die obtaining a number at random from to
. What is the probability that Diana's number is larger than Apollo's number?
Solution
Note that the probability of Diana rolling a number larger than Apollo's is the same as the probability of Apollo's being more than Diana's. If we denote this common probability , then
Apollo=Diana
. Now all we need to do is find
Apollo=Diana
. There are
possibilities total, and 6 of those have Apollo=Diana, so
Apollo=Diana
. Going back to our first equation and solving for D, we get