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, then probability that neither A nor B happens is
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
As our answer does not match with any other option
But option of none of these is there. So most suitable option is option (d)
∴ Option (d) is the only correct choice.