In probability theory, an elementary event or atomic event is a singleton of a sample space. An outcome is an element of a sample space. An elementary event is a set containing exactly one outcome, not the outcome itself. However, elementary events are often written as outcomes for simplicity when the difference is unambiguous.
The following are examples of elementary events:
Elementary events may have probabilities that are strictly positive, zero, undefined, or any combination thereof. For instance, any discrete probability distribution is determined by the probabilities it assigns to what may be called elementary events. In contrast, all elementary events have probability zero under any continuous distribution. Mixed distributions, being neither entirely continuous nor entirely discrete, may contain atoms. Atoms can be thought of as elementary (that is, atomic) events with non-zero probabilities. Under the measure-theoretic definition of a probability space, the probability of an elementary event need not even be defined, since mathematicians distinguish between the sample space S and the events of interest, defined by the elements of a σ-algebra on S.