2016 AIME I Problems/Problem 2
Problem 2
Two dice appear to be normal 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
It is easier to think of the dice as sided dice with sixes, fives, etc. Then there are possible rolls. There are rolls that will result in a seven. The odds are therefore . The answer is
See also
2016 AIME I (Problems • Answer Key • Resources) | ||
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Followed by Problem 3 | |
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