3-32. LetA1, . . . ,An be a set of events defined on S. Suppose S = ∪ni

=1Ai, P(Ai) >

0 for all i and Ai ∩ Aj = φ, i
= j. Then for any event B, verify that P(B) = ni

=1 P(B|Ai ) · P(Ai). (Hint: Use the distributive lawA∩(B∪C) =

(A ∩ B) ∪ (A ∩ C).)