Question

Three fair dice are rolled together at the same time. Find the probability of the three numbers appearing on the tops being a prime number.

Answer 1

Dear Student,
$$\begin{gathered} Primenumbersare2,3and5. \\ Allpossibletripletswiththreediceshowingprimenumbersare \\ (2,2,2),(2,,2,3),(2,2,5),(2,3,2),(2,3,3),(2,3,5),(2,5,2),(2,5,3),(2,5,5), \\ (3,2,2),(3,2,3),(3,2,5),(3,3,2),(3,3,3),(3,3,5),(3,5,2),(3,5,3),(3,5,5), \\ (5,2,2),(5,2,3),(5,2,5),(5,3,2),(5,3,3),(5,3,5),(5,5,2),(5,5,3),(5,5,5). \\ Theseareall27caseseachwithprobability\frac{1}{6^3}=\frac{1}{216}. \\ Hence,therequiredprobabilityis=\frac{27}{216}=\boxed{\frac{\mathbf{1}}{\mathbf{8}}} \end{gathered}$$
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