Problem:
When a certain unfair die is rolled, an even number is 3 times as likely to appear as an odd number. The die is rolled twice. What is the probability that the sum of the numbers rolled is even?
Answer Choices:
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Solution:
Suppose that the probability of rolling an odd number is . The probability of rolling an even number is then . Because , it follows that , so the probability of rolling an odd number is and the probability of rolling an even number is . The sum will be even if both rolls are even or both rolls are odd. Therefore the probability of rolling an even sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions