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AMO · 2027 · Grades 8-9 · Self-study SET 23 Question 7

AMO

Question 7

A semiprime is a number $p_1p_2$, where $p_1,p_2$ are primes; they may be equal. Three independent fair standard six-sided dice are rolled. The probability that their sum is semiprime is $a/b$ in lowest terms, with $a,b>0$. Find $a+b$.