# Total Probability and Bayes's Theorem

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This Demonstration provides examples of total probability and Bayes's theorem. In the given world a figure X is randomly chosen. What is the probability of the given statement S? Suppose the statement is true. What is the probability that X = A? What is the probability that X = B?

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Contributed by: Izidor Hafner (March 2011)

Open content licensed under CC BY-NC-SA

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## Details

The conditional probability of an event A assuming that B has occurred, denoted P(A|B), equals P(A|B)=(P(A ⋂ B))/(P(B)). If P(B)=0, P(A|B) is undefined.

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