If P(A) , P(B) = and P(A ∪ B) = , find (i) P(A ∩ B) (ii) P(A|B) (iii) P(B|A)

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Solution

The given probabilities are,

P( A )= 6 11 , P( B )= 5 11 and P( A∪B )= 7 11 .

(i)

The probability ( A∩B ) can be calculated as,

P( A∩B )=P( A )+P( B )−P( A∪B ) = 6 11 + 5 11 − 7 11 =1− 7 11 = 4 11

Therefore, the value of P( A∩B )= 4 11 .

(ii)

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

P( A|B )= P( A∩B ) P( B ) = 4 11 5 11 = 4 5

Therefore, the value of P( A|B )is 4 5 .

(iii)

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

P( B|A )= P( A∩B ) P( A ) = 4 11 6 11 = 4 6 = 2 3

Therefore, the value of P( B|A )is 2 3 .

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