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Question

Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6 Find
P (neither A nor B)

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Solution

It is given that P(A) = 0.3 and P(B) = 0.6
Also, A and B are independent events.
P( neigther A and B) = P(A' and B')
=P(AB)=P(AB)=1P(AB)=10.72=0.28
Alternatively,
P(neither A nor B)=P(AB)=P(A)P(B)
( A and B are independent , A' and B' are also independent)
=[1P(A)][1P(B)]=(10.3)(10.6)=0.7×0.4=0.28


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