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Question: If A and B an two events such that \(P ( A \cup B ) = \frac { 5 } { 6 }\) , \(P ( A \cap B ) = \fra...

If A and B an two events such that P(A∪B)=56P ( A \cup B ) = \frac { 5 } { 6 } , P(A∩B)=13P ( A \cap B ) = \frac { 1 } { 3 } and P(Bˉ)=13P ( \bar { B } ) = \frac { 1 } { 3 } then P(A)=P ( A ) =

A

14\frac { 1 } { 4 }

B

13\frac { 1 } { 3 }

C

12\frac { 1 } { 2 }

D

23\frac { 2 } { 3 }

Answer

12\frac { 1 } { 2 }

Explanation

Solution

P(A)=P(A∩B)+P(A∪B)−P(B)P ( A ) = P ( A \cap B ) + P ( A \cup B ) - P ( B )