### Probability Theory, Bayes's theorem

Consider now the defining relation (4) for the conditional probability P(An|B), where the Ai are mutually exclusive and their union is the entire sample space. Substitution of P(An)P(B|An) in the numerator of (4) and substitution of the right-hand side of the law of total probability in the denominator yields a result known as Bayes's theorem (after the 18th-century English clergyman Thomas Bayes)

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