Question: Let A and B be two events with P(B) > 0, and let C1,C2, ... be a possible partition of a sample space. Prove or

Let A and B be two events with P(B) > 0, and let C1,C2, ... be a possible partition of a sample space. Prove or disprove the following formulas:

P(A|B) = 

i P(A|B ∩ Ci)P(Ci), P(A|B) = 

i P(A|B ∩ Ci)P(B|Ci)P(Ci).

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