Problem:
Two fair coins are to be tossed once. For each head that results, one fair die is to be rolled. What is the probability that the sum of the die rolls is odd? (Note that if no die is rolled, the sum is .)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If one die is rolled, of the possible numbers are odd. If two dice are rolled, of the possible outcomes have odd sums. In each of these cases, the probability of an odd sum is . If no die is rolled, the sum is , which is not odd. The probability that no die is rolled is equal to the probability that both coin tosses are tails, which is . Thus the requested probability is
The problems on this page are the property of the MAA's American Mathematics Competitions