Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6 Find
P (neither A nor B)
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(A′∩B′)=P(A∪B)′=1−P(A∪B)=1−0.72=0.28
Alternatively,
P(neither A nor B)=P(A′∩B)=P(A)P(B)
(∵ A and B are independent , ∴ A' and B' are also independent)
=[1−P(A)][1−P(B)]=(1−0.3)(1−0.6)=0.7×0.4=0.28