Problem:
A pair of six-sided fair dice are labeled so that one die has only even numbers (two each of , and ), and the other die has only odd numbers (two each of , and ). The pair of dice is rolled. What is the probability that the sum of the numbers on the tops of the two dice is ?
Answer Choices:
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Solution:
The sum could be only if the even die showed and the odd showed , the even showed and the odd showed , or the even showed and the odd showed . Each of these events can occur in ways. Hence there are ways for a to occur. There are possible outcomes, so the probability that a occurs is .
The problems on this page are the property of the MAA's American Mathematics Competitions