Collectively exhaustive events

When given a set of two or more events, if at least one of the events must occur, then such a set of events is said to be collectively exhaustive.

Consider the following examples:

• Given a set of events {temperature < 60, temperature > 90}, these events are not collectively exhaustive because there is a third option that is not given in this set of events: The temperature could be between 60 and 90. However, they are mutually exhaustive because both cannot happen at the same time.

• In a dice roll, the set of events of rolling a {1, 2, 3, 4, 5, or 6} are collectively exhaustive because these are the only possible events, and at least one of them must happen.