In probability theory, a set of events is collectively exhaustive if at least one of the events must occur. For example, when rolling a six-sided die, the outcomes 1, 2, 3, 4, 5, and 6 are collectively exhaustive, because they encompass the entire range of possible outcomes. Probability theory is the mathematical study of probability. ... Rolling dice A die (Old French de, from Latin datum something given or played [1]) is a small polyhedral object (usually a cube) suitable as a gambling device (especially for craps or sic bo). ...

Compare this to the concept of a set of outcomes which are mutually exclusive, which means that at most one of the events must occur. The set of all possible die rolls is both collectively exhaustive and mutually exclusive. In probability theory, events E1, E2, ... , En are said to be mutually exclusive if the occurrence of any one them automatically implies the non-occurrence of the remaining n-1 events. ...