If P(A∩B)=12,P(A¯∩B¯)=13,P(A)=p,P(B)=2p, then the value of p is given by

Since, P(A¯∩B¯)=13⇒ P(A∪B¯)=13 ⇒ 1−P(A∪B)=13⇒ P(A∪B)=23 ⇒ P(A)+P(B)−P(A∩B)=23⇒ p+2p−12=23

If P(A∩B)=12,P(A¯∩B¯)=13,P(A)=p,P(B)=2p, then the value of p is given by

Since, P(A¯∩B¯)=13⇒ P(A∪B¯)=13 ⇒ 1−P(A∪B)=13⇒ P(A∪B)=23 ⇒ P(A)+P(B)−P(A∩B)=23⇒ p+2p−12=23

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If $P (A \cap B) = \frac{1}{2}, P (\bar{A} \cap \bar{B}) = \frac{1}{3}, P (A) = p, P (B) = 2 p,$ then the value of p is given by

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$\frac{1}{3}$

$\frac{7}{18}$

$\frac{4}{9}$

$\frac{1}{2}$

answer is B.

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Since, $P (\bar{A} \cap \bar{B}) = \frac{1}{3} \Rightarrow P (\bar{A \cup B}) = \frac{1}{3} \Rightarrow 1 - P (A \cup B) = \frac{1}{3}$

$\Rightarrow P (A \cup B) = \frac{2}{3} \Rightarrow P (A) + P (B) - P (A \cap B) = \frac{2}{3} \Rightarrow p + 2 p - \frac{1}{2} = \frac{2}{3}$

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If P(A∩B)=12,P(A¯∩B¯)=13,P(A)=p,P(B)=2p, then the value of p is given by

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If $P (A \cap B) = \frac{1}{2}, P (\bar{A} \cap \bar{B}) = \frac{1}{3}, P (A) = p, P (B) = 2 p,$ then the value of p is given by