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If `P(A cap B)=(1)/(2), P(overline(A) cap overline(B))=(1)/(2)` and 2P(A)=P(B)=p, then the value of p is equal to

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If P(A∩B)= 1 2 ,P( ˉ A ∩ ˉ B )= 1 2 and 2P(A)=P(B)=p, then the value of p is equal to A. 1 2 B. 2 3 C. 1 4 D. 1 3 Select the correct answer from above options

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Correct Answer - B We have, P(A∩B)= 1 2 ,P( ˉ A ∩ ˉ B )= 1 2 and2P(A)-P(B)=p Now, P( ˉ A ∩ ˉ B )= 1 2 ⇒P( ¯ A∪B )= 1 2 ⇒1-P(A∪B)= 1 2 ⇒P(A∪B)= 1 2 ⇒P(A)+P(B)-P(A∩B)= 1 2 ⇒ p 2 +p- 1 2 = 1 2 ⇒ 3p 2 =1⇒p= 2 3

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