Bayes’ theorem



Let (An) be a sequence of mutually exclusive eventsMathworldPlanetmath whose union ( is the sample space and let E be any event. All of the events have nonzero probability (P(E)>0 and P(An)>0 for all n). Bayes’ Theorem states


for any Aj(An).

A simpler formulation is:


For two events, A and B (also with nonzero probability).


  • 1 Milton, J.S., Arnold, Jesse C., Introduction to Probability and Statistics: Principles and Applications for Engineering and the Computing Sciences, McGraw Hill, 1995.
Title Bayes’ theorem
Canonical name BayesTheorem
Date of creation 2013-03-22 12:02:13
Last modified on 2013-03-22 12:02:13
Owner akrowne (2)
Last modified by akrowne (2)
Numerical id 11
Author akrowne (2)
Entry type Theorem
Classification msc 60-00
Classification msc 62A01
Synonym Bayes’ Rule
Related topic ConditionalProbability