Law of total probability

If \(\{B_n:n=1, 2, 3, \ldots\}\) is a finite partition of a sample space (i.e., a set of pairwise disjoint events whose union is the entire sample space), then for any event A of the same probability space:
$$Pr(A) = \sum_n Pr(A\cap B_n)$$
or, alternatively,
$$Pr(A) = \sum_n Pr(A|B_n)Pr(B_n)$$