University of California, San Diego: Edward Bender and S. Williamson's "Lists, Decisions, and Graphs: Decision Trees and Recursion"

Read Section 3 on pages DT-28 through DT-35.

Bayes' theorem is a famous theorem for computing conditional probabilities. Assume Ei are mutually exclusive events for i = 1,..., n and Ui Ei = D, for arbitrary event D, P(Ei | D) = P(D | Ei ) P(Ei) / [P(D|E1)P( E1) + ....+ P(D|En) P(En)]. Statements of Bayes' theorem are given on pages DT-28 and DT-32. Like the binomial theorem, Bayes' theorem is very useful in calculating probabilities for many applications, for example, in diagnosis and in decision theory.

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