Editing Mutual exclusivity (section)

{{short description|Two propositions or events that cannot both be true}}
{{About|logical exclusivity of events and propositions|the concept in concurrent computing|Mutual exclusion|the concept in developmental psychology|Mutual exclusivity (psychology)}}
{{More footnotes needed|date=October 2009}}
{{Probability fundamentals}}

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 events|collectively exhaustive]], which means that at least one of the outcomes must happen, so these two possibilities together exhaust all the possibilities.<ref>{{cite book |last=Miller |first=Scott |first2=Donald |last2=Childers |title=Probability and Random Processes |publisher=Academic Press |edition=Second |year=2012 |page=8 |isbn=978-0-12-386981-4 |quote=The sample space is the collection or set of 'all possible' distinct (collectively exhaustive and mutually exclusive) outcomes of an experiment. }}</ref> 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).