Question

The probabilities of happening of two events A and B are 0.25 and 0.50 respectively. If the probability of happening of A and B together is 0.14, then probability that neither A nor B happens is
(a) 0.39
(b) 0.25
(c) 0.11
(d) none of these

Answer 1

(a) 0.39
Given:
P(A) = 0.25, P(B) = 0.50 and P(A$\cap$B) = 0.14
∴ Required probability = 1 $-$P(A∪B)
= 1 $-$ [P(A) + P(B) $-$ P(A$\cap$B)]
= 1 $-$ [0.25 + 0.50 $-$ 0.14]
= 1 $-$ 0.61 = 0.39