In probability theory, an elementary event or atomic event is a subset of a sample space that contains only one element of the sample space. It is important to note that an elementary event is still a set containing an element of the sample space, not that element itself. However, elementary events are often written as elements rather than sets for simplicity, where this is unambiguous.
Examples of sample spaces, S, and elementary events include:
- If objects are being counted, and the sample space S = {0, 1, 2, 3, ...} (the natural numbers), then the elementary events are all sets {k}, where k ∈ N.
- If a coin is tossed twice, S = {HH, HT, TH, TT}, H for heads and T for tails, and the elementary events are {HH}, {HT}, {TH} and {TT}.
- If X is a Gaussian random variable, S = (-∞, +∞), the real numbers, and the elementary events are all sets {x}, where x ∈ R.