Exhaustive events are a set of events in a sample space such that at least one of them must occur whenever the experiment is performed. In other words, the union of all the events in the set is equal to the sample space of the experiment. Exhaustive events can be represented using Venn diagrams, where the circles represent the events and their union represents the sample space.

Exhaustive events can be classified into two types: mutually exclusive and non-mutually exclusive. Mutually exclusive events are disjoint events, meaning they do not have any outcomes in common. On the other hand, non-mutually exclusive events can overlap.

Examples of exhaustive events include rolling a die, where the events 1, 2, 3, 4, 5, and 6 are collectively exhaustive because they encompass the entire range of possible outcomes. Another example is tossing a coin, where the outcomes of heads and tails are collectively exhaustive and mutually exclusive.

In summary, exhaustive events are a set of events that cover all possible outcomes of an experiment, and at least one of them must occur whenever the experiment is performed.