​ The probability of occurrence of two events A and B are 1/4 and 1/2 respectively. ​

Question

The probability of occurrence of two events A and B are \(\frac{1}{4}\) and \(\frac{1}{2}\) respectively. The probability of their simultaneous occurrence is \(\frac{7}{50}\). What is the probability that neither A nor B occurs. 

[Hint:find 1- P(A∪3)]

Answer 1

Given P(A) = \(\frac{1}{4}\), P(B) = \(\frac{1}{2}\)

P(A∩ B) = \(\frac{7}{5}\)

P(neither A nor B) = P(A’∩B’) = P(A∪B)’ 

= 1 – P(A∪B) 

=1 – [P(A)+P(B)-P(A∩B)]