Final answer:
Two events are mutually exclusive if one happening means the other cannot. These events cannot occur at the same time and the probability of them occurring together is zero.
Step-by-step explanation:
Two events are mutually exclusive if by virtue of one event happening the other cannot happen. Mutually exclusive events do not share any outcomes, which means they cannot occur simultaneously. If events A and B are mutually exclusive, then the probability of A and B happening at the same time, denoted as P(A AND B), is zero.
For an example to illustrate this, let's consider rolling a six-sided die. The event A could be rolling an even number, while event B could be rolling an odd number. These two events are mutually exclusive because a single die roll cannot result in both an even and an odd number.
In contrast, independent events, such as the outcomes of two separate rolls of a fair die, do not affect each other's probabilities. The knowledge that one independent event occurred does not change the likelihood of the second occurring. Independent events satisfy conditions like P(A AND B) = P(A)P(B).