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If the set S is divided into subsets B_1, B_2 which B_1 ∪ B_2 = S, B_1 ∩ B_2 = ∅ and P(B_1) gt; 0 and P(B_2) gt; 0, then for any event A ⊂ S below formula is true. P(A) = P(A|B_1) * P(B_1) + P(A|B_2) * P(B_2). Derivation. The sets A ∩ B_1 and A ∩ B_2 are disjoint because B_1 ∩ \cap B_2 = ∅, thus from the definition of the probability. From the conditional probability.