Elementary event

In probability theory, an elementary event (also called an atomic event or sample point) is an event which contains only a single outcome in the sample space. Using set theory terminology, an elementary event is a singleton. Elementary events and their corresponding outcomes are often written interchangeably for simplicity, as such an event corresponding to precisely one outcome.

The following are examples of elementary events:

• All sets $\{k\},$ where $k\in \mathbb {N}$ if objects are being counted and the sample space is $S=\{1,2,3,\ldots \}$ (the natural numbers).
• $\{HH\},\{HT\},\{TH\},{\text{ and }}\{TT\}$ if a coin is tossed twice. $S=\{HH,HT,TH,TT\}.$ H stands for heads and T for tails.
• All sets $\{x\},$ where $x$ is a real number. Here $X$ is a random variable with a normal distribution and $S=(-\infty ,+\infty ).$ This example shows that, because the probability of each elementary event is zero, the probabilities assigned to elementary events do not determine a continuous probability distribution.