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Let A, B, C be pariwise independent events with `P(C) >0 and P(AnnBnnC) = 0`. Then `P(A^c nn B^c/C)`.

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Let A, B, C be pariwise independent events with P(C)>0andP(A∩B∩C)=0 . Then P(Ac∩ Bc C ) . A. P(Ac)+P(Bc) B. P(Ac)-P(Bc) C. P(Ac)-P(B) D. P(A)-P(Bc) Select the correct answer from above options

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Correct Answer - C P ( A c ∩ B c / C ) P = P ( ( A ∪ B ) c R C ) = = 1 − P ( ( A ∪ B ) / C ) = 1 − P ( ( A ∪ B ) ∩ C ) P ( C ) = = 1 − P ( A ∩ C ) ∪ ( B ∩ C ) P ( C ) = = 1 − { P ( A ∩ C ) + P ( B ∩ C ) − P ( A ∩ B ∩ ) } P ( C ) = = 1 − { P ( A ) P ( C ) + P ( B ) P ( C ) − 0 P ( C ) } = = 1 − { P ( A ) + P ( B ) } = 1 − P ( A ) − P ( B ) = P ( A c ) − P ( B ) =

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