Final answer:
The claim that two events are mutually exclusive if they occur simultaneously is false; mutually exclusive events cannot occur at the same time, and their joint probability is zero.
Step-by-step explanation:
The statement that two events are said to be mutually exclusive if they occur simultaneously is false. Mutually exclusive events are those events that cannot occur at the same time, which means that the occurrence of one event precludes the occurrence of the other event. In probability, P(A AND B) for mutually exclusive events is equal to 0. Independent events, on the other hand, are events where the occurrence of one event does not affect the probability of occurrence of another event.
For example, when rolling a die, the events of rolling a 2 and rolling a 5 are mutually exclusive, as both cannot happen simultaneously in a single roll. However, the event of rolling a 2 and flipping a coin landing on heads are independent events, as one does not influence the probability of the other.