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.

Proofs: 1

  1. Problem: Broken Items in the Box

Solutions: 1


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References

Bibliography

  1. Bosch, Karl: "Elementare Einf├╝hrung in die Wahrscheinlichkeitsrechnung", vieweg Studium, 1995, 6th Edition