Law of total probability

In mathematics, the law of total probability states that if <math>A</math> and <math>B</math> are events, then

<math>P(B) = P(B|A)P(A) + P\left(B|A^c\right)P\left(A^c\right)</math>

(see )

In general, if <math>A_1, \ldots, A_n</math> are mutually exclusive events that partition the sample space, and <math>B</math> is any event, then

<math>P(B) = \sum_{i=1}^n P\left(B|A_i\right) P\left(A_i\right)</math>

(see )