Question

# Given two independent events A and B such that P (A) = 0.3, P (B) = 0.6. Find (i) P (A and B) (ii) P (A and not B) (iii) P (A or B) (iv) P (neither A nor B)

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Solution

## (i) The probability of A is 0⋅3 and the probability of B is 0⋅6. The formula for two independent events is, P( A∩B )=P( A )⋅P( B ) Substitute the given values in the above formula we get, P( A∩B )=0⋅3×0⋅6 =0⋅18 Thus, the value of P( A∩B )=0⋅18. (ii) The probability of ( A and not B ) or P( A∩B' ) is, P( A∩ B ′ )=P( A )−P( A∩B ) =0.3−0.18 =0.12 Thus, the value of P( A∩B' )=0.12. (iii) The formula of P( A∪B ) is, P( A∪B )=P( A )+P( B )−P( A∩B ) Substitute the given values in the above formula we get, P( A∪B )=0.3+0.6−0.18 =0.9−0.18 =0.72 Thus, the value of P( A∪B )=0.72. (iv) The formula probability of (neither A nor B) or P( A ′ ∩ B ′ ) is, P( A ′ ∩ B ′ )=P ( A∪B ) ′ =1−P( A∪B ) Substitute the given values in the above formula we get, P( A ′ ∩ B ′ )=1−0.72 =0.28 Thus, the value of P( A ′ ∩ B ′ )=0.28.

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