First slide

Theorems of probability

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

Moderate

A

0.39
B

0.25
C

0.11
D

None of these

Solution

$\begin{array}{l} P (A \cup B) = P (A) + P (B) - P (A \cap B) \\ = 0.25 + 0.50 - 0.14 \\ = 0.61 \\ ∴ P (A^{'} \cap B^{'}) = P ((A \cup B)^{'}) = 1 - P (A \cup B) \\ = 1 - 0.61 = 0.39 \end{array}$

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