Evaluate P (A ∪ B), if 2P (A) = P (B) = and P(A|B) =

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Solution

The probabilities are given as,

2P( A )=P( B )= 5 13 and P( A|B )= 2 5 .

As 2P( A )= 5 13 , so, P( A )= 5 26 .

The probability P( A∩B ) is calculated as,

P( A∩B )=P( B )⋅P( A|B ) = 5 13 ( 2 5 ) = 2 13

The probability P( A∪B ) is calculated as,

P( A∪B )=P( A )+P( B )−P( A∩B ) = 5 26 + 5 13 − 2 13 = 5+10−4 26 = 11 26

Therefore, the value of P( A∪B )is 11 26 .

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