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Question

Let Ec denotes the complement of an event E. If E, F, G are pairwise independent evens with P(G) > 0 and P(EFG)=0. Then, P(EcFc|G) equals

A
P(Ec)+P(Fc)
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B
P(Ec)P(Fc)
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C
P(Ec)P(F)
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D
P(E)P(Fc)
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Solution

The correct option is C P(Ec)P(F)
P(EcFc|G)=P(EcFcG)P(G)=P(G)P(EG)P(GF)P(G) [P(G)0]=1P(E|G)P(F|G)=1P(E)P(F) [ E, F, G are pairwise independent]=P(Ec)P(F)

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