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.^[1] 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 ${\displaystyle \{k\},}$ where ${\displaystyle k\in \mathbb {N} }$ if objects are being counted and the sample space is ${\displaystyle S=\{1,2,3,\ldots \}}$ (the natural numbers).
• ${\displaystyle \{HH\},\{HT\},\{TH\},{\text{ and }}\{TT\}}$ if a coin is tossed twice. ${\displaystyle S=\{HH,HT,TH,TT\}}$ where ${\displaystyle H}$ stands for heads and ${\displaystyle T}$ for tails.
• All sets ${\displaystyle \{x\},}$ where ${\displaystyle x}$ is a real number. Here ${\displaystyle X}$ is a random variable with a normal distribution and ${\displaystyle S=(-\infty ,+\infty ).}$ 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.