Final answer:
When given that events A and B are mutually exclusive, the probability that both A and B occur simultaneously is P(A AND B) = 0. So, the correct answer to the question is A) 0.0.
Step-by-step explanation:
If Event A has a probability of 0.4 of occurring and Event B has a probability of 0.5 of occurring, and we know that A and B are mutually exclusive events, this means that they cannot happen at the same time.
The probability of an event occurring is a number between 0 and 1, where 0 indicates that the event will not occur, and 1 indicates that the event is certain to occur. In this case, event A has a probability of 0.4 of occurring, and event B has a probability of 0.5 of occurring.
2. **Mutually Exclusive Events**: Events are said to be mutually exclusive, or disjoint, if they cannot occur at the same time. In other words, the occurrence of one event excludes the possibility of the other event happening simultaneously.
3. **Probability of Mutually Exclusive Events Occurring Together**: Since mutually exclusive events cannot occur at the same time, the probability of both events A and B occurring together is 0.
So, to answer the question: The probability that both mutually exclusive events A and B occur, which is denoted P(A and B), is 0.0. The correct answer is: A) 0.0The definition of mutually exclusive implies that the probability that both events occur, denoted as P(A AND B), is 0. So, the correct answer to the question is A) 0.0.