Before giving the Bayes theorem statement is important to define the conditional probability. Once done, the Bayes theorem is easy to derive. Conditional Probability The conditional probability measures the likelihood of an event given that another event has occurred. For instance, assuming that A is the event of interest and that B consists of a different event which has already occurred. The probability of the event A to occur, given the occurrence of B , (written as) P ( A | B ), can be computed as detailed by the following equality. P(A | B) = P(A ∩ B) / P(B) P( B ) > 0 (1) It is defined as the quotient of the probability of the joint events A and B and the probability of B . Now consider P(B | A), which is equals to P(B ∩ A) / P(A). Since P(B ∩ A) = P(A ∩ B), then the fo...
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