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Let $0 < P (A) < 1, 0 < P (B) < 1$ and $P (A \cup B) = P (A) + P (B) - P (A) P (B)$ then which of the following is correct?

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PBA=P(B)−P(A)

P(A¯∪B¯)=P(A¯)+P(B¯)

P(A∪B¯)=P(A¯)P(B¯)

PAB=P(A)

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detailed solution

Correct option is C

We know thatP(A∪B)=P(A)+P(B)−P(A∩B)∴ Here, P(A∩B)=P(A)P(B)⇒ A, B are independent events.⇒A, Bc¯; Ac, B and Ac¯, Bc¯ also pairwise independent events.∴P(A∪B¯)=P(A¯∩B¯)=P(A¯)P(B¯) and P(A/B)=P(A∩B)P(B)=P(A).

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Let 0<P(A)<1, 0<P(B)<1 and P(A∪B)=P(A)+P(B)−P(A)P(B) then which of the following is correct?

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Let $0 < P (A) < 1, 0 < P (B) < 1$ and $P (A \cup B) = P (A) + P (B) - P (A) P (B)$ then which of the following is correct?