Collectively exhaustive events

In probability theory and logic, a set of events is jointly or collectively exhaustive if at least one of the events must occur. For example, when rolling a six-sided die, the events 1, 2, 3, 4, 5, and 6 (each consisting of a single outcome) are collectively exhaustive, because they encompass the entire range of possible outcomes. In probability theory and logic, a set of events is jointly or collectively exhaustive if at least one of the events must occur. For example, when rolling a six-sided die, the events 1, 2, 3, 4, 5, and 6 (each consisting of a single outcome) are collectively exhaustive, because they encompass the entire range of possible outcomes. Another way to describe collectively exhaustive events is that their union must cover all the events within the entire sample space. For example, events A and B are said to be collectively exhaustive if where S is the sample space. Compare this to the concept of a set of mutually exclusive events. In such a set no more than one event can occur at a given time. (In some forms of mutual exclusion only one event can ever occur.) The set of all possible die rolls is both mutually exclusive and collectively exhaustive (i.e., 'MECE'). The events 1 and 6 are mutually exclusive but not collectively exhaustive. The events 'even' (2,4 or 6) and 'not-6' (1,2,3,4, or 5) are collectively exhaustive but not mutually exclusive. In some forms of mutual exclusion only one event can ever occur, whether collectively exhaustive or not. For example, tossing a particular biscuit for a group of several dogs cannot be repeated, no matter which dog snaps it up.