Statistics and Probability Glossary
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Bayes Rule
Bayes' theorem (also known as Bayes' rule) is a very useful tool for calculating
conditional probabilities
. Bayes' theorem can be stated as follows:
Bayes' theorem. Let A 1, A 2,
... , A n be a set of mutually exclusive events that together form
the sample space S. Let B be any event from the same sample space, such that
P(B) > 0. Then,
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P( Ak | B ) =
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P( Ak ∩ B )
P( A1 ∩ B ) + P( A2 ∩ B ) + . . . + P( An ∩ B )
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Note: Invoking the fact that P( A k ∩ B ) = P( A k )P( B | A k ), Bayes' theorem can
also be expressed as
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P( Ak | B ) =
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P( Ak ) P( B | Ak )
P( A1 ) P( B | A1 ) + P( A2 ) P( B | A2
) + . . . + P( An ) P( B | An )
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