Outcome (probability)

In probability theory, an outcome is a possible result of an experiment. Each possible outcome of a particular experiment is unique, and different outcomes are mutually exclusive (only one outcome will occur on each trial of the experiment). All of the possible outcomes of an experiment form the elements of a sample space.

For the experiment where we flip a coin twice, the four possible outcomes that make up our sample space are (H, T), (T, H), (T, T) and (H, H), where "H" represents a "heads", and "T" represents a "tails". Outcomes should not be confused with events, which are sets (or informally, "groups") of outcomes. For comparison, we could define an event to occur when "at least one 'heads'" is flipped in the experiment - that is, when the outcome contains at least one 'heads'. This event would contains all outcomes in the sample space except the element (T, T).

Since individual outcomes may be of little practical interest, or because there may be prohibitively (even infinitely) many of them, outcomes are grouped into sets of outcomes that satisfy some condition, which are called "events." The collection of all such events is a sigma-algebra.

An event containing exactly one outcome is called an elementary event. 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.

Typically, when the sample space is finite, any subset of the sample space is an event (i.e. all elements of the power set of the sample space are defined as events). However, this approach does not work well in cases where the sample space is uncountably infinite (most notably when the outcome must be some real number). So, when defining a probability space it is possible, and often necessary, to exclude certain subsets of the sample space from being events.

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