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jmc

counting and probability junior

Problem

Adam rolled two standard six-sided dice once. What is the probability that he did not roll a prime number on either die? Express your answer as a common fraction.
Solution
The prime numbers from 1 to 6 are 2, 3, and 5. Thus, the probability of Adam not rolling a prime number on any one die is equal to , since there is an equal probability of rolling any number from 1 to 6. Since the two dice are independent, the probability of Adam not rolling a prime number on either die is equal to .
Final answer
\frac{1}{4}