Welcome guest
You're not logged in.
283 users online, thereof 0 logged in

## Theorem: Law of Total Probability

Given mutually exclusive and collectively exhaustive events $$A_1,A_2,\ldots,A_n$$ with the probabilities $$p(A_i) > 0$$ for $$i=1,2,\ldots,n$$, the probability of any event $$B$$ can be calculated by the formula

$p(B)=\sum_{i=1}^np(B|A_i)p(A_i)=p(B|A_1)p(A_1) + p(B|A_2)p(A_2) + \ldots + p(B|A_n)p(A_n).$

This formula is called the law of total probability.

| | | | | created: 2014-02-23 22:45:22 | modified: 2017-08-04 23:07:13 | by: bookofproofs | references: [856]

(none)