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Probability: compound events and complements
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Learn it For "at least one", use the complement: P(at least one) = 1 − P(none). For two independent events, multiply. Without replacement, the second probability changes.
Example: A number cube is rolled twice. P(at least one 6)?
- P(no 6 either time) $= \frac{5}{6} \times \frac{5}{6} = \frac{25}{36}$.
- P(at least one 6) $= 1 - \frac{25}{36}$.
- $= \frac{11}{36}$.
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