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Question

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

A
P(Ee)+P(Fe)
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B
P(Ee)P(Fe)
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C
P(Ee)P(F)
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D
P(E)P(Fe)
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Solution

The correct option is C P(Ee)P(F)
Given: P(Ee)=1P(E) and E, F, G are pairwise independent events, P(G)>0, P(EFG)=0
To find: P(EeFe|G)=?
Sol:
P(EeFe|G)=P(EeFeG)P(G)=P(Ee)P(Fe)P(G)P(G)=P(Ee)P(Fe)=P(Ee)[1P(F)]=P(Ee)P(Ee)P(F)=P(Ee)[1P(E)]P(F)=P(Ee)P(F)+P(E)P(F)
E, F, G are independent and P(EFG)=0
P(E)P(F)P(G)=0 but P(G)0
P(E)P(F)=0
Hence P(EeFe|G)=P(Ee)P(F)

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