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In mathematics, the '''law of total probability''' states that if <math>A</math> and <math>B</math> are [[event]]s, then
<center><math>P(B) = P(B|A)P(A) + P\left(B|A^c\right)P\left(A^c\right)</math></center>
(see <ref>Ghahramani, Saeed. ''Fundamentals of Probability: With Stochastic Processes''. 3rd ed. Upper Saddle River (NJ): Pearson Prentice Hall, 2005. p. 88</ref>)
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
<center><math>P(B) = \sum_{i=1}^n P\left(B|A_i\right) P\left(A_i\right)</math></center>
(see <ref>Ghahramani, p. 93</ref>)
==References==
<refererences />
<center><math>P(B) = P(B|A)P(A) + P\left(B|A^c\right)P\left(A^c\right)</math></center>
(see <ref>Ghahramani, Saeed. ''Fundamentals of Probability: With Stochastic Processes''. 3rd ed. Upper Saddle River (NJ): Pearson Prentice Hall, 2005. p. 88</ref>)
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
<center><math>P(B) = \sum_{i=1}^n P\left(B|A_i\right) P\left(A_i\right)</math></center>
(see <ref>Ghahramani, p. 93</ref>)
==References==
<refererences />