Difference between revisions of "FidgetBoss 4000's 2019 Mock AMC 12B Problems/Problem 4"

(Created page with "<i>(fidgetboss_4000)</i> 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}{1...")
 
 
Line 1: Line 1:
 +
==Problem==
 
<i>(fidgetboss_4000)</i> Mark rolled two standard dice. Given that he rolled two distinct values, find the probability that he rolled two primes.
 
<i>(fidgetboss_4000)</i> 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}{5}\qquad\textbf{(D) }\frac{2}{5}\qquad\textbf{(E) }\frac{1}{2}\qquad</math>
 
<math>\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</math>

Latest revision as of 23:04, 19 November 2020

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, $\frac{3}{15}=\boxed{\textbf{(C) }\frac{1}{5}}$

See also

FidgetBoss 4000's 2019 Mock AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions

The problems on this page are copyrighted by FidgetBoss 4000's Mock American Mathematics Competitions. AMC logo.png