Basic events (also called atomic events or simple events) are events that have a single result only in the sample space. In set theory terms, a basic event is a singleton. For simplicity, basic events and their corresponding results are usually interchangeable, because such events are completely equivalent to a result. The most basic and indecomposable results that can be directly observed in the experiment are called basic events.

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The probability (probability) that a basic event may occur between zero and one. In the discrete probability distribution with limited sample space, each basic event is given a specific probability. On the contrary, in continuous distribution, a single basic event must have zero probability, because there are infinitely many, so non-zero probability can only be assigned to non-basic events.

Some "mixed" distributions contain two continuous basic events and some discrete basic events; The discrete basic events in this distribution can be called atoms or atomic events, and they can have non-zero probability.

Under the definition of measure theory in probability space, it is not necessary to define the probability of basic events. In particular, the set of events defining probability can be some σ algebras on S, but not necessarily the complete set.