Problem-Solving and Data AnalysisVery hardAt least one six in three rolls
Problem-Solving and Data Analysis practice question
A fair six-sided die is rolled three times. What is the probability that at least one of the rolls shows a six?
Answer: 91/216
P(no six in three rolls) = (5/6)³ = 125/216, so P(at least one six) = 1 − 125/216 = 91/216.
Common wrong answers
- If you answered 1/2
- 1/2 adds 1/6 three times, which overcounts rolls with more than one six.
- If you answered 1/216
- 1/216 is the probability of three sixes.
- If you answered 125/216
- 125/216 is the probability of no sixes at all.
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