FidgetBoss 4000's 2019 Mock AMC 12B Problems/Problem 4

Problem

(fidgetboss_4000) Mark rolled two standard dice. Given that he rolled two distinct values, find the probability that he rolled two primes. $\textbf{(A) }\frac{1}{12}\qquad\textbf{(B) }\frac{1}{7}\qquad\textbf{(C) }\frac{1}{5}\qquad\textbf{(D) }\frac{2}{5}\qquad\textbf{(E) }\frac{1}{2}\qquad$

Solution

There are $\binom{6}{2}=15$ different ways Mark could roll two distinct values. There are $\binom{3}{2}=3$ ways Mark could roll two distinct primes. Then, $\frac{3}{15}=\boxed{\textbf{(C) }\frac{1}{5}}$

FidgetBoss 4000's 2019 Mock AMC 12B (Problems • Answer Key • Resources)
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FidgetBoss 4000's 2019 Mock AMC 12B Problems/Problem 4

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