Bayes's theorem

A simple form of Bayes's theorem is

, where A′ denotes the complementary event (see sample space) to the event A. For example, suppose a man has two coins in his pocket. One is unbiased, whereas the other is double headed. He takes one coin at random from his pocket and tosses it. Given that the coin falls heads, the probability that it is the double-headed coin is


. The general form is


, where the events A₁, A₂,..., A_n are mutually exclusive and exhaustive.

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