Let Ec denotes the complement of an event E. If E, F, G are pairwise independent evens with P(G) > 0 and P(E∩F∩G)=0. Then, P(Ec∩Fc|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 CP(Ec)−P(F) P(Ec∩Fc|G)=P(Ec∩Fc∩G)P(G)=P(G)−P(E∩G)−P(G∩F)P(G)[∵P(G)≠0]=1−P(E|G)−P(F|G)=1−P(E)−P(F)[∵E,F,Garepairwiseindependent]=P(Ec)−P(F)