Law of total probability

In mathematics, the law of total probability states that if $A$ and $B$ are events, then

$P(B)=P(B|A)P(A)+P\left(B|A^{c}\right)P\left(A^{c}\right)$

(see )

In general, if $A_{1},\ldots ,A_{n}$ are mutually exclusive events that partition the sample space, and $B$ is any event, then

$P(B)=\sum _{i=1}^{n}P\left(B|A_{i}\right)P\left(A_{i}\right)$

(see )