Question

Two events A and B have probabilities 0.25 and 0.50, respectively. The probability that both A and B occur simultaneously is 0.14. Then, the probability that neither A nor B occurs, is ______.

Options

• 0.39

• 0.25

• 0.11

• None of these

Answer 1

Two events A and B have probabilities 0.25 and 0.50, respectively. The probability that both A and B occur simultaneously is 0.14. Then, the probability that neither A nor B occurs, is 0.39.

Explanation:

Given, P(A) = 0.25, P(B) = 0.50

and P(A ∩ B) = 0.14

∴ P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

= 0.25 + 0.50 – 0.14

= 0.61

Now, `P(overline(A ∪ B))` = 1 – P(A ∪ B)

= 1 – 0.61

= 0.39