Question

A and B are two events where P(A)=0.25 and P(B)=0.5. The probability of both happening together is 0.14. The probability of both A and B not happening is

A) 0.39
B) 0.25
C) 0.11
D) NONE OF THESE

Answer 1

The probability of both A and B not happening is calculated using the complement of the probability of either event occurring. Using the complement rule and the given probabilities, the correct answer is found to be 0.39.

Step-by-step explanation:

We're given that P(A) = 0.25, P(B) = 0.5, and P(A AND B) = 0.14. To find the probability of both A and B not happening, we need to use the complement rule. The complement rule states that the probability of an event not occurring is 1 minus the probability of the event occurring.

First, we can find the probability of at least one of A or B occurring, which is P(A OR B). This can be found using the formula P(A OR B) = P(A) + P(B) - P(A AND B).

So we have P(A OR B) = 0.25 + 0.5 - 0.14 = 0.61. Now, since we want to find the probability of neither A nor B happening, which is the complement of P(A OR B), we do the following calculation: 1 - P(A OR B) = 1 - 0.61 = 0.39.

Therefore, the probability of both A and B not happening is 0.39.