When we say that two events, A and B, are mutually exclusive, we mean that they cannot occur at the same time. In more technical terms, the occurrence of one event means that the other event cannot happen. For example, if A is the event of rolling a 2 on a die, and B is the event of rolling a 4, then A and B are mutually exclusive.
The probability of the intersection of two events, denoted as P(A ∩ B), measures the chance that both events occur simultaneously. However, because A and B cannot happen at the same time due to their mutual exclusivity, the probability of A intersection B is zero.
Thus, we can represent this mathematically as:
P(A ∩ B) = 0
This means that if you know two events are mutually exclusive, you can confidently state that the probability of both occurring at the same time is always zero.