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
Solutions: 1