Define exclusive events.

Exclusive events, also known as mutually exclusive events, are events that cannot occur at the same time or overlap in any way. In other words, if one event happens, the other event cannot happen simultaneously. The occurrence of one event precludes the occurrence of the other.

Mathematically, if we have two events A and B, they are considered exclusive if the probability of their intersection (the probability that both events occur) is zero. Symbolically, if P(A ∩ B) = 0, then A and B are exclusive events.

For example, let's consider the events "rolling an even number on a fair six-sided die" (event A) and "rolling an odd number on the same die" (event B). Since the outcomes of rolling a die can only result in either an even or an odd number, these two events are exclusive. If you roll the die and get an even number, it is impossible to get an odd number at the same time.

In general, exclusive events represent situations where the occurrence of one event guarantees the non-occurrence of the other event.