2019 Mock AMC 10B Problems/Problem 6: Difference between revisions
Created page with "==Problem== 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\t..." |
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<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> | <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> | ||
==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}{6} \cdot \frac{3}{6} = \boxed{\text{(C)} \frac{1}{6}}</math>. | |||
Latest revision as of 20:46, 25 October 2025
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 
.
