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In statistics, the law of total probability is that "the prior probability of A is equal to the prior expected value of the posterior probability of A." That is, for any random variable ,

where is the conditional probability of A given N.

Law of alternativesEdit

The term law of total probability is sometimes taken to mean the law of alternatives, which is a special case of the law of total probability applying to discrete random variables. It is the proposition that if { B_n : n = 1, 2, 3, ... } is a finite or countably infinite partition of a probability space and each set B_n is measurable, then for any event A we have

or, alternatively,

See alsoEdit

• law of total expectation
• law of total variance
• law of total cumulance

de:Totale Wahrscheinlichkeit]]

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