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Total Probability Theorem

The total probability theorem, also called the law of total probability or total probability rule, states that, given n mutually exclusive events A_1, ..., A_n whose probabilities sum to unity,

P(B)=P(B|A_1)P(A_1)+...+P(B|A_n)P(A_n),

where B is an arbitrary event, and P(B|A_i) is the conditional probability of B assuming A_i.

See also

Bayes' Theorem, Conditional Probability, Inclusion-Exclusion Principle, Mutually Exclusive Events

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References

Papoulis, A. Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, pp. 37-38, 1984.

Referenced on Wolfram|Alpha

Total Probability Theorem

Cite this as:

Weisstein, Eric W. "Total Probability Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TotalProbabilityTheorem.html

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