Final answer:
For mutually exclusive events A and B with probabilities P(A) = .50 and P(B) = .30, the probability of their intersection P(A ∩ B) is 0. Since mutually exclusive events cannot occur simultaneously, the correct answer to the question is C. 0.
Step-by-step explanation:
When dealing with the concepts of probability and events, it's important to understand the difference between mutually exclusive and independent events. In probability theory, two events, A and B, are mutually exclusive if they cannot occur at the same time. That is, the occurrence of one event prevents the other from occurring, which implies that the probability of both events occurring together, P(A ∩ B), is 0.
If we have P(A) = .50 and P(B) = .30, and we know A and B are mutually exclusive, then P(A ∩ B), or the probability of both A and B occurring, is straightforward to determine. As per the rules of probability for mutually exclusive events, the probability of the intersection of A and B, denoted by P(A AND B), is simply 0. This essentially means there is no chance that both events A and B will happen at the same time.
So, given the options provided (A. .5, B. .6, C. 0, D. .06), the correct answer is C. 0. Remember, although the individual probabilities of A and B are given as 0.50 and 0.30 respectively, these values do not influence the probability of the intersection of A and B when they are mutually exclusive since the very definition of being mutually exclusive means that one event's occurrence completely rules out the occurrence of the other.