Question: 9. Let (,S,P) be a probability space. Let A, B, C S with PB and PC > 0. If B and C are independent

9. Let (Ω,S,P) be a probability space. Let A, B, C ∈ S with PB and PC > 0. If B and C are independent show that P{A | B} = P{A | B∩C}PC+P{A | B∩Cc}PCc.

Conversely, if this relation holds, P{A | BC} = P{A | B}, and PA > 0, then B and C are independent (Strait [111]).

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