Law of total probability

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In mathematics, the law of total probability states that if $\text{[math]}$ and $\text{[math]}$ are events, then

\text{[math]}

(see ^[1])

In general, if $\text{[math]}$ are mutually exclusive events that partition the sample space, and $\text{[math]}$ is any event, then

\text{[math]}

(see ^[2])

References

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

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Mathematics