Hifumi's Study NotesnotesProbability and StatisticsMultiplicative Rule

Multiplicative Rule

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Cegep/2

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The cardinality of an event that occurs through a series of $k$ mutually exclusive events is

n (A_{1} \cap A_{2} \cap \dots A_{k}) = n (A_{1}) n (A_{2}) \dots n (A_{k})

Multiplicative rule of probability

The probability of an event that occurs through a series of $k$ mutually exclusive events is

For independent events, $P (A_{1} \cap A_{2} \cap \dots A_{k}) = P (A_{1}) P (A_{2}) \dots P (A_{k})$
For dependent events, $P (A_{1} \cap A_{2} \cap \dots A_{k}) = P (A_{1}) P (A_{2} | A_{1}) \dots P (A_{k} | A_{k - 1} \cap \dots A_{1})$

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