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}{ | + | <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{ | + | 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>. |
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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.
Solution
Each die has 
prime numbers: 
. Since the numbers rolled on each die must be distinct, the answer is 
.
