# Law of total probability

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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

- de:Totale Wahrscheinlichkeit]]
- it:Teorema della probabilità totale]]
- zh:全概率公式]]

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