User:Birdlover1234

The law of total probability is a theorem that states, in its discrete case, if $$\left\{{B_n : n = 1, 2, 3, \ldots}\right\}$$ is a finite or countably infinite partition of a sample space (in other words, a set of pairwise disjoint events whose union is the entire sample space) and each event $$B_n$$ is measurable, then for any event $$A$$ of the same sample space:


 * $$P(A)=\sum_n P(A\cap B_n)$$

or, alternatively,


 * $$P(A)=\sum_n P(A\mid B_n)P(B_n),$$

where for any $$n$$ for which $$P(B_n) = 0 $$ these terms are simply omitted from the summation since $$P(A\mid B_n)$$ is finite.