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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 ...
An event, however, is any subset of the sample space, including any singleton set (an elementary event), the empty set (an impossible event, with probability zero) and the sample space itself (a certain event, with probability one). Other events are proper subsets of the sample space that contain multiple elements. So, for example, potential ...
Here, an "event" is a set of zero or more outcomes; that is, a subset of the sample space. An event is considered to have "happened" during an experiment when the outcome of the latter is an element of the event. Since the same outcome may be a member of many events, it is possible for many events to have happened given a single outcome.
The red oval is the event that a number is odd, and the blue oval is the event that a number is prime. A sample space can be represented visually by a rectangle, with the outcomes of the sample space denoted by points within the rectangle. The events may be represented by ovals, where the points enclosed within the oval make up the event. [12]
The event that contains all possible outcomes of an experiment is its sample space. A single outcome can be a part of many different events. [4] Typically, when the sample space is finite, any subset of the sample space is an event (that is, all elements of the power set of the sample space are defined as
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A probability is a way of assigning every event a value between zero and one, with the requirement that the event made up of all possible results (in our example, the event {1,2,3,4,5,6}) is assigned a value of one. To qualify as a probability, the assignment of values must satisfy the requirement that for any collection of mutually exclusive ...
A set of events, where each event is a set containing zero or more outcomes. The assignment of probabilities to the events—that is, a function P mapping from events to probabilities. An outcome is the result of a single execution of the model.