A and B are two events such that P(A) = 0.54, P(B) = 0.69 and P(A ∩ B) = 0.35. Find (i) P(A ∩ B) (ii) P(A′ ∩ B′) (iii) P(A ∩ B′) (iv) P(B ∩ A′)

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Solution

Let, the two events Aand B such that,

P( A )=0.54 P( B )=0.69 P( A∩B )=0.35

(i)

The value of P( A∪B ) is calculated as follows,

P( A∪B )=P( A )+P( B )−P( A∩B ) P( A∪B )=0.54+0.69−0.35 P( A∪B )=0.88

(ii)

The value of P( A ′ ∩ B ′ ) is calculated as follows,

P( A ′ ∩ B ′ )=P ( A∪B ) ′ =1−P( A∪B ) =1−0.88 P( A ′ ∩ B ′ )=0.12

(iii) P( A∩ B ′ )

The value of P( A∩ B ′ )is calculated as follows,

P( A∩ B ′ )=P( A )−P( A∩B ) =0.54−0.35 P( A∩ B ′ )=0.19

(iv) P( B∩ A ′ )

The value of P( B∩ A ′ )is calculated as follows,

P( B∩ A ′ )=P( B )−P( A∩B ) =0.69−0.35 P( B∩ A ′ )=0.34

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