independent events

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Two events (see sample space) A and B are independent if

P(AB)=P(A) × P(B),

or, equivalently, if P(A|B)=P(A), or if P(B|A)=P(B). Three events A, B, and C are said to be independent (or mutually independent) if each pair is independent and if, in addition,

P(ABC)=P(A) × P(B) × P(C).

For a set of more than three events to be independent the multiplication rule must hold for all possible subsets. See also conditional probability; intersection; pairwise independent.

Subjects: Probability and Statistics.

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