Editing Elementary event (section)

{{redirect2|Basic outcome|Atomic event|atomic events in computer science|linearizability}}

{{Probability fundamentals}}
In [[probability theory]], an '''elementary event''', also called an '''atomic event''' or '''sample point''', is an [[Event (probability theory)|event]] which contains only a single [[Outcome (probability)|outcome]] in the [[sample space]].<ref>{{cite book|last=Wackerly|first=Denniss|author2=William Mendenhall|author3=Richard Scheaffer|title=Mathematical Statistics with Applications|year=2002 |publisher=Duxbury|isbn=0-534-37741-6}}</ref> Using [[set theory]] terminology, an elementary event is a [[Singleton (mathematics)|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 <math>\{ k \},</math> where <math>k \in \N</math> if objects are being counted and the sample space is <math>S = \{ 1, 2, 3, \ldots \}</math> (the [[natural numbers]]).
* <math>\{ HH \}, \{ HT \}, \{ TH \}, \text{ and } \{ TT \}</math> if a coin is tossed twice. <math>S = \{ HH, HT, TH, TT \}</math> where <math>H</math> stands for heads and <math>T</math> for tails.
* All sets <math>\{ x \},</math> where <math>x</math> is a  [[real number]]. Here <math>X</math> is a [[random variable]] with a [[normal distribution]] and <math>S = (-\infty, + \infty).</math> 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]]..