Product formula

Rearranging the definition of conditional probability we obtain an expression for the probability of the intersection of two events.

Property — Product formula

$P(A \cap B) = P(B) \cdot P(A \mid B) = P(A) \cdot P(B \mid A).$

The two ways of writing it show that we can decompose the intersection starting equally from $A$ or from $B$: we choose the one for which the probabilities are easier to compute.

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Topics: Probability
Concepts: Product formula · Conditional probability
Skills: Using formulae