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title: "Probability event notation"
canonical: "https://modelassist.epixanalytics.com/space/EA/26574943/Probability%20event%20notation"
format: markdown
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The following notation is developed from set theory and is used extensively to represent probabilities of events and their relationships.
| | | |
| --- | --- | --- |
| ### Notation | ### Explanation | ### Statistical term |
| > Macro (inline-media-image)
> Macro (mathinline) | The probability that event A occurs | Marginal probability |
| > Macro (inline-media-image)
> Macro (mathinline)
or > Macro (inline-media-image)
> Macro (mathinline) | The probability that event A does not occur. AC is called the complement of A. > Macro (inline-media-image)
> Macro (mathinline) | Complement |
| 
> Macro (mathinline) | The probability that events A **and** B both occur | Joint probability |
| 
> Macro (mathinline) | The probability that either events A **or** B occur | Probability union |
| 
> Macro (mathinline) | The probability that event A occurs **given** that event B has occurred | Conditional probability |
| 
> Macro (mathinline) | A and B are mutually exclusive events i.e. they can't exist together | Disjoint probability |
| 
> Macro (mathinline) | The null event, i.e. impossibility so, for example > Macro (inline-media-image)
> Macro (mathinline)
and > Macro (inline-media-image)
> Macro (mathinline) | Null probability |
| 
> Macro (mathinline) | The probability of all events Ai occurring | Joint probabilities |
| 
> Macro (mathinline) | The probability of any event Ai occurring | Union of probabilities |
| 
> Macro (mathinline) | e is the set of all possible things (i.e. anything), so P(e) = 1 | - |
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