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Difference between revisions of "2019 Mock AMC 10B Problems/Problem 6"

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Mark rolled two standard dice. Given that he rolled two distinct values, find the probability that he rolled two primes.
 
Mark rolled two standard dice. Given that he rolled two distinct values, find the probability that he rolled two primes.
  
<math>\textbf{(A)}\ \frac{1}{12}\qquad\textbf{(B)}\ \frac{1}{7}\qquad\textbf{(C)}\ \frac{1}{6}\qquad\textbf{(D)}\ \frac{1}{2}\qquad\textbf{(E)}\ \frac{2}{5}</math>
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<math>\textbf{(A)}\ \frac{1}{12}\qquad\textbf{(B)}\ \frac{1}{7}\qquad\textbf{(C)}\ \frac{1}{5}\qquad\textbf{(D)}\ \frac{1}{2}\qquad\textbf{(E)}\ \frac{2}{5}</math>
  
 
==Solution==
 
==Solution==
  
Each die has <math>3</math> prime numbers: <math>2, 3, 5</math>. Since the numbers rolled on each die must be distinct, the answer is <math>\frac{3}{6} \cdot \frac{2}{6} = \boxed{\text{(C)} \frac{1}{6}}</math>.
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Each die has <math>3</math> prime numbers: <math>2, 3, 5</math>. Since the numbers rolled on each die must be distinct, the answer is <math>\frac{2}{5} \cdot \frac{3}{6} = \boxed{\text{(C)} \frac{1}{5}}</math>.

Latest revision as of 16:09, 27 August 2020

Problem

Mark rolled two standard dice. Given that he rolled two distinct values, find the probability that he rolled two primes.

$\textbf{(A)}\ \frac{1}{12}\qquad\textbf{(B)}\ \frac{1}{7}\qquad\textbf{(C)}\ \frac{1}{5}\qquad\textbf{(D)}\ \frac{1}{2}\qquad\textbf{(E)}\ \frac{2}{5}$

Solution

Each die has $3$ prime numbers: $2, 3, 5$. Since the numbers rolled on each die must be distinct, the answer is $\frac{2}{5} \cdot \frac{3}{6} = \boxed{\text{(C)} \frac{1}{5}}$.

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