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Probability of Product Being Prime

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January 14, 2009
probability

Problem Statement

Twelve fair dice are rolled. What is the probability that the product of the numbers on the top faces is prime? <spanclass=′latex−bold′>(A)</span> (112)12<spanclass=′latex−bold′>(B)</span> (16)12<spanclass=′latex−bold′>(C)</span> 2(16)11<spanclass=′latex−bold′>(D)</span> 52(16)11<spanclass=′latex−bold′>(E)</span> (16)10 <span class='latex-bold'>(A)</span>\ \left(\frac{1}{12}\right)^{12}\qquad <span class='latex-bold'>(B)</span>\ \left(\frac{1}{6}\right)^{12}\qquad <span class='latex-bold'>(C)</span>\ 2\left(\frac{1}{6}\right)^{11}\qquad <span class='latex-bold'>(D)</span>\ \frac{5}{2}\left(\frac{1}{6}\right)^{11}\qquad <span class='latex-bold'>(E)</span>\ \left(\frac{1}{6}\right)^{10}
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