If ` 0 lt P(A) lt 1, 0 lt P(B) lt 1` and `P(A cup B)=P(A)+P(B)-P(A)P(B)`, then

Question

If 0 < P ( A ) < 1 , 0 < P ( B ) < 1 and P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ) P ( B ) , then A. P ( A / B ) = P ( A ) + P ( B ) B. P ( A ∪ B ) c = P ( A c ) P ( B c ) C. P ( A c − B c ) = P ( A c ) P ( B c ) D. P ( B / A ) = P ( B ) − P ( A ) Select the correct answer from above options

Answer 1

Correct Answer - B We have, P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ) P ( B ) P ⇒ P ( A ) + P ( B ) − P ( A ∩ B ) = P ( A ) + P ( B ) − P ( A ) P ( B ) ⇒ ⇒ P ( A ∩ B ) = P ( A ) P ( B ) ⇒ ⇒ ⇒ A and B are independent events ⇒ A c and B c ⇒ are independent events ⇒ ( A c ∩ B c ) = P ( A c ) P ( B c ) ⇒ ⇒ P ( A ∪ B ) c = P ( A c ) P ( B c ) ⇒ Hence, option (b) is true.