Law of total probability

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

(see [1])

In general, if are mutually exclusive events that partition the sample space, and is any event, then

(see [2])


  1. Ghahramani, Saeed. Fundamentals of Probability: With Stochastic Processes. 3rd ed. Upper Saddle River (NJ): Pearson Prentice Hall, 2005. p. 88
  2. Ghahramani, p. 93