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Mutually exclusive events
From Wikipedia, the free encyclopedia
In simple terms, two events are mutually exclusive if they cannot occur at the same time (i.e. they have no outcomes in common).
In logic, two mutually exclusive (or "mutual exclusive" according to some sources) propositions are propositions that logically cannot both be true. To say that more than two propositions are mutually exclusive may, depending on context mean that no two of them can both be true, or only that they cannot all be true. The term pairwise mutually exclusive always means no two of them can both be true.
In probability theory, events E1, E2, ..., En are said to be mutually exclusive if the occurrence of any one of them automatically implies the non-occurrence of the remaining n − 1 events. Therefore, two mutually exclusive events cannot both occur. Mutually exculsive events have the property: Pr(A ∩ B) = 0. For example, the result "1" and "2" from the roll of a dice are mutually exclusive, because it cannot be a 1 and a 2. Similarly, "heads" and "tails" from the toss of a coin are mutually exclusive as they cannot happen at the same time.
In short, mutual exclusivity implies that at most one of the events may occur. Compare this to the concept of being collectively exhaustive, which means that at least one of the events must occur.