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In Probability Theory , events ''E''1, ''E''2, ..., ''E''''n'' are said to be mutually exclusive if the occurrence of any one them automatically implies the non-occurrence of the remaining ''n'' − 1 events. In other words, two mutually exclusive events cannot both occur.

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.


EXAMPLES

  • A flipped coin coming up heads and the same coin coming up tails at the same time are mutually exclusive events.

  • A student passing a test and failing it are mutually exclusive (though someone can fail a test, retake it, and then pass- or have the grade scaled).

  • When rolling a six-sided die, each of the outcomes 1, 2, 3, 4, 5 and 6 are mutually exclusive ''and'' collectively exhaustive, because no more than one outcome can occur simultaneously and they encompass the entire range of possible outcomes.

  • The logical operation A XOR B means A and B are mutually exclusive and cannot both be true at the same time. In order for A XOR B to be true, either A or B must be true but not both.



SEE ALSO