Skip to main content
OlympiadHQ

Browse · MATH

Print

jmc

counting and probability intermediate

Problem

Two different integers from 1 through 20 inclusive are chosen at random. What is the probability that both numbers are prime? Express your answer as a common fraction.
Solution
There are pairs of distinct integers between 1 and 20, and there are pairs of distinct prime numbers between 1 and 20. Therefore, the probability that both members of a randomly chosen pair are prime is .
Final answer
\dfrac{14}{95}