# Event (probability theory)

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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.[1] A single outcome may be an element of many different events,[2] and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes.[3] 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 ${\displaystyle x\in S}$).[4] 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?