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If `P(A cap B)=1//3, P(A cup B)=5//6 " and " P(A)=1//2`, then which one of the following is correct ?

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If P(A∩B)=1/3,P(A∪B)=5/6 and P(A)=1/2, then which one of the following is correct ? A. A and B are independent events B. A and B are mutually exclusive events C. P(A)=P(B) D. P(A)<P(B) Select the correct answer from above options

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Correct Answer - A We have, P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ∩ B ) P ⇒ 5 6 = 1 2 + P ( B ) − 1 3 ⇒ P ( B ) = 2 3 ⇒ Clearly, P ( A ∩ B ) = P ( A ) P ( B ) P So, A and B are independent events.

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