: Mathématiques: event

probability theory > event

event

In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. 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 consisting of only a single outcome is called an elementary event or an atomic event; that is, it is a singleton set. An event that has more than one possible outcomes is called compound event. An event ${\\displaystyle S}$ is said to occur if ${\\displaystyle S}$ contains the outcome ${\\displaystyle x}$ of the experiment (or trial) (that is, if ${\\displaystyle x\\in S}$ ). The probability (with respect to some probability measure) that an event ${\\displaystyle S}$ occurs is the probability that ${\\displaystyle S}$ contains the outcome ${\\displaystyle x}$ of an experiment (that is, it is the probability that ${\\displaystyle x\\in S}$ ). 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?
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Event_(probability_theory))

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