Skip to main content
OlympiadHQ

Browse · MATH

Print

jmc

counting and probability senior

Problem

John rolls a pair of standard 6-sided dice. What is the probability that the two numbers he rolls are relatively prime? Express your answer as a common fraction.
Solution
We have to use a little bit of casework to solve this problem. If the first die shows a 1, the second die can be anything (6 cases). If the first die shows 2 or 4, the second die is limited to 1, 3, or 5 ( cases). If the first die shows 3, the second die can be 1, 2, 4, or 5 (4 cases). If the first die shows 5, the second die can be anything but 5 (5 cases). If the first die shows 6, the second die can be only 1 or 5 (2 cases). There are 36 ways to roll two dice, 23 of which are valid, so the answer is .
Final answer
\frac{23}{36}