Karl Jones: Created page with "In probability theory, an '''event''' is a set of outcomes of an experiment (a subset..."

2016-09-14T03:02:00Z

Created page with "In probability theory, an '''event''' is a set of outcomes of an experiment (a subset..."

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In [[probability theory]], an '''event''' is a [[Set (mathematics)|set]] of [[Outcome (probability)|outcomes]] of an [[Experiment (probability theory)|experiment]] (a [[subset]] of the [[sample space]]) to which a [[probability]] is assigned.

== Description ==

A single outcome may be an element of many different events, and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes.

An event defines a [[complementary event]], namely the complementary set (the event not occurring), and together these define a [[Bernoulli trial]]: did the event occur or not?

Typically, when the sample space is finite, any subset of the sample space is an event (i.e. all elements of the [[power set]] of the sample space are defined as events).

However, this approach does not work well in cases where the sample space is [[Uncountable set|uncountably infinite]], most notably when the outcome is a [[real number]]. So, when defining a probability space it is possible, and often necessary, to exclude certain subsets of the sample space from being events.

== See also ==

* [[Bernoulli trial]]
* [[Complementary event]]
* [[Elementary event]]
* [[Independent event]]
* [[Probability space]]
* [[Probability theory]]

== External links ==

* [https://en.wikipedia.org/wiki/Event_(probability_theory) Event (probability theory)] @ Wikipedia.org

[[Category:Mathematics]]

Event (probability theory) - Revision history

Karl Jones: Created page with "In probability theory, an '''event''' is a set of outcomes of an experiment (a subset..."