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In probability theory, an elementary event (also called an atomic event or simple event) 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 corresponds to precisely one outcome. The following are examples of elementary events: * All sets , where ''k'' ∈ N if objects are being counted and the sample space is ''S'' = (the natural numbers). * , , and if a coin is tossed twice. ''S'' = . H stands for heads and T for tails. * All sets , where ''x'' is a real number. Here ''X'' is a random variable with a normal distribution and ''S'' = (−∞, +∞). 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. ==Probability of an elementary event== Elementary events may occur with probabilities that are between zero and one (inclusively). In a discrete probability distribution whose sample space is finite, each elementary event is assigned a particular probability. In contrast, in a continuous distribution, individual elementary events must all have a probability of zero because there are infinitely many of them— then non-zero probabilities can only be assigned to non-elementary events. Some "mixed" distributions contain both stretches of continuous elementary events and some discrete elementary events; the discrete elementary events in such distributions can be called atoms or atomic events and can have non-zero probabilities. Under the measure-theoretic definition of a probability space, the probability of an elementary event need not even be defined. In particular, the set of events on which probability is defined may be some σ-algebra on ''S'' and not necessarily the full power set. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Elementary event」の詳細全文を読む スポンサード リンク
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