Bayes' Theorem

Bayes' Theorem evaluates the probability of an event conditional upon another event of known probability having taken place.

Suppose B1, ..., Bn are a set of mutually exclusive events coving the entire sample space and A is an event that has been observed.

The probability that the event Bj is the causal event giving rise to A, i.e. the probability of Bj conditional upon A, is given by Bayes' theorem, which states:

Pr(Bj | A) =
Pr(Bj) Pr(A | Bj)
Pr(Bi) Pr(A | Bi)


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