Problem:
Two dice appear to be standard dice with their faces numbered from to , but each die is weighted so that the probability of rolling the number is directly proportional to . The probability of rolling a with this pair of dice is , where and are relatively prime positive integers. Find .
Solution:
Because , the probability of rolling a with one of these dice is . Then the probability of rolling a with the pair of dice is
The requested sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions