Bayes’s Theorem of Conditional Probability

by Max Andrews

Thomas Bayes’s theorem, in probability theory, is a rule for evaluating the conditional probability of two or more mutually exclusive and jointly exhaustive events.  The conditional probability of an event is the probability of that event happening given that another event has already happened.[1]  The theorem may be expressed as:


What the solution [P(h|e&k)] represents is the probability of the hypothesis in question is given the evidence and the background information.  The numerator [P(e|h&k) P(h|k)]  is the probability of the product of evidence and background knowledge and the background knowledge alone. The denominator [P(e|k)] is the probability of the event with the evidence alone.  Each factor involved is assigned a probability between 0 and 1 with 0 as impossible and 1 being completely certain.[2]

[1] Patrick J. Hurley, Logic (Belmont, CA:  Thomson Wadsworth, 2008), 519.

[2] For an in depth look at Bayes’ Theorem applied to arguments, particularly theistic arguments, see Richard Swinburne, The Existence of God (Oxford:  Oxford University Press, 2004) 66-72.


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