Bayes' Theorem

For 2 events

Suppose We say B1 and B2 partition S. Then one and only one of the events, B1 or B2 must occur when the random experiment is observed.

Suppose A is any other event, and suppose further that are all known.

Bayes' theorem tells us how to compute P(B1|A) and P(B2|A).

P(B1|A) = from the definition of conditional probability

= by the multiplication rule for probabilities

= is Bayes' theorem.

The denominator of Bayes' theorem is P(A). By a similar argument

P(B2|A) =

= 1- P(B1|A).

A tree diagram is a useful aid in representing Bayes' theorem.

Examples: Binary Communication Channel Airport Threat

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