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Complements and "at least one"
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Learn it "At least one" is usually easiest through the complement: P(at least one) = 1 − P(none).
Example: A die is rolled 3 times. P(at least one 6)?
- P(no 6 in one roll) = $\frac{5}{6}$.
- P(no 6 in three rolls) = $\left(\frac{5}{6}\right)^3 = \frac{125}{216}$.
- P(at least one 6) = $1 - \frac{125}{216} = \frac{91}{216}$.
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