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2008 AMC 10B Problem 16

Problem 16 of 25IntermediateNumber TheoryCounting & Probability

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 0.0.)

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Solution

Whenever at least one die is rolled, by symmetry the sum is odd with probability 12.\tfrac12. No die is rolled only when both coins are tails, with probability 14;\tfrac14; that sum 00 is even. So the answer is (114)12=38.\left(1-\tfrac14\right)\cdot\tfrac12=\tfrac38. Thus, the correct answer is A.

More practice

Concepts: conditional probability · dice (probability) · parity

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