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Let $A_1,\ldots,A_n$ be a partition of a sample space $S$ with $P(A_i) > 0$ 
for all $i$,
and let $B$ be an event in $S$.  Then
$$P(B) = P(B|A_1)P(A_1) + \ldots + P(B|A_n)P(A_n).$$
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