A fair die is rolled twice. What is the probability that at least one of the two rolls shows a 4?

Step-by-step solution

1. Identify the complementary event: neither roll shows a 4.
2. The probability that a single roll is not a 4 is $5/6$ because there are 5 other faces.
3. Since the two rolls are independent, the probability that neither roll shows a 4 is $(5/6)\times (5/6)=25/36$.
4. The probability of the desired event is the complement: $1-25/36=11/36$.
5. Hence the required probability is $11/36$.

Concept tested: Complementary event probability with independent trials

Published 4 October 2026 · How this solution was prepared and checked