Q18 of 28 Page 16

The probabilities of happening of two events. A and B are 0.25 and 0.50 respectively. If the probability of happing of A and B together is 0.14, find the probability that neither A nor B happens.

Given, P(A) = 0.25 and P(B) = 0.5


Also P(A ∩ B) = 0.14


We have to find P(A’ ∩ B’)


By De Morgan’s theorem we know that:


P(A’ ∩ B’) = P(A ∪ B)’


We know that P(A ∪ B) = P(A) + P(B) – P(A ∩ B)


∴ P(A ∪ B) = 0.25 + 0.5 – 0.14 = 0.61


∴ P (A’ ∩ B’) = P(A ∪ B)’ = 1 -P(A ∪ B) = 1 – 0.61 = 0.39


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