A and B are two events such that P(A) = 0.25 and P(B) = 0.50. The probability of both happening together is 0.14. The probability of both A and B not happening is

Question

Philoid · Accepted Answer

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 matches with option (a)

∴ Option (a) is the only correct choice.