Probability

# Law of Total Probability

## Keywords:

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

or

$P\left(A\right)=P\left(A|{B}_{1}\right)·P\left({B}_{1}\right)+P\left(A|{B}_{2}\right)·P\left({B}_{2}\right)+...+P\left(A|{B}_{n}\right)·P\left({B}_{n}\right)$

where

$\sum _{i=1}^{n}{B}_{i}={B}_{1}+{B}_{2}+...+{B}_{n}=\Omega$

is a complete system of events.