Let Ai be any events. a) Show that P(A1 ∩A2 ∩A3) = P(A1 ∩A2 ∩A3) = P(A1)·P(A2 | A1)·P(A3 | A1 ∩A2)

Question: Let Ai be any events.

a) Show that P(A1 ∩A2 ∩A3) = P(A1 ∩A2 ∩A3) = P(A1)·P(A2 | A1)·P(A3 | A1 ∩A2) .

b) Generalize this to give a formula for the intersection of any number of events. [Hint: Use induction.]

Solution: