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In probability theory, an event is a subset of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. [1] A single outcome may be an element of many different events, [2] and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. [3]
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 ...
Beta distribution, for a single probability (real number between 0 and 1); conjugate to the Bernoulli distribution and binomial distribution Gamma distribution , for a non-negative scaling parameter; conjugate to the rate parameter of a Poisson distribution or exponential distribution , the precision (inverse variance ) of a normal distribution ...
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
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.
In the latter two examples the law of total probability is irrelevant, since only a single event (the condition) is given. By contrast, in the example above the law of total probability applies, since the event X = 0.5 is included into a family of events X = x where x runs over (−1,1), and these events are a partition of the probability space.
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The marginal probability is the probability of a single event occurring, independent of other events. A conditional probability, on the other hand, is the probability that an event occurs given that another specific event has already occurred. This means that the calculation for one variable is dependent on another variable. [2]
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