Mutual exclusivity

In logic and probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur at the same time. A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both.

In the coin-tossing example, both outcomes are, in theory, collectively exhaustive, which means that at least one of the outcomes must happen, so these two possibilities together exhaust all the possibilities.[1] However, not all mutually exclusive events are collectively exhaustive. For example, the outcomes 1 and 4 of a single roll of a six-sided die are mutually exclusive (both cannot happen at the same time) but not collectively exhaustive (there are other possible outcomes; 2,3,5,6).

  1. ^ Miller, Scott; Childers, Donald (2012). Probability and Random Processes (Second ed.). Academic Press. p. 8. ISBN 978-0-12-386981-4. The sample space is the collection or set of 'all possible' distinct (collectively exhaustive and mutually exclusive) outcomes of an experiment.

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