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Question:

Let A, B and C be three events, which are pair-wise independent and ¬E denotes the complement of an event E. If P(A∩B∩C) = 0 and P(C) > 0, then P[(¬A∩¬B)|C] is equal to.

P(¬A) + P(¬B)

P(A) + P(¬B)

P(¬A) - P(¬B)

P(¬A) - P(B)

Solution:

we need find P(¬A∩¬B|C) = shaded portions in Venn Diagram = P(¬A∩¬B|C) = P(¬A∩¬B∩C)/P(C) = P(C) - P(A∩C) - P(B∩C)/P(C) = 1 - P(A).P(C) + P(B).P(C)/P(C) = 1 - P(A) - P(B) = P(¬A) - P(B)