What is the probability of P(AUB), if P(A) = 0.23, P(B) = 0.41, and P(
AB) = 0.12?

(assuming that .)

Step-by-step explanation:

The question is asking for the probability of the event ( or , or both.)

Refer to the diagram attached. There are three mutually-exclusive ways to satisfy :

Probability that is satisfied but isn't:

.

Probability that and are both satisfied:

.

Probability that is satisfied but isn't:

.

There's no intersection between these three ways for satisfying . Hence, the probability would be the sum of the probability of each of the three ways:

.

Instead of calculating and separately, the work above may be condensed into one equation:

.

a. is correct