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Event

An event is a subset of the set of all possible outcomes of a probabilistic experiment.

The set of all possible outcomes is called sample space and it is usually denoted by Omega. Thus, an event E is a subset of Omega, which is indicated by[eq1]

In simple probabilistic settings, all subsets of the sample space are considered events. However, there are also more complicated settings in which some subsets of the sample space cannot be considered events.

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Example

If the probabilistic experiment is the roll of a dice, the set of all possible outcomes is[eq2]In this setting, three instances of events are[eq3]Event A could be described in words as "An odd number appears face up", event $B$ could be described as "A number strictly greater than four appears face up", and event $C$ could be described as "The number $2$ appears face up".

More details

For examples and more detailed explanations of the concept of event, you can go to the lecture entitled Probability.

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