Outcome (probability)

Lore & Background

Outcomes are the fundamental building blocks of probability theory. For example, in the experiment of flipping a coin twice, the four possible outcomes are (H, T), (T, H), (T, T), and (H, H). Outcomes should not be confused with events, which are sets or groups of outcomes. An event such as 'at least one heads' contains all outcomes except (T, T).

Reader's Guide

Outcomes are central to probability theory as they form the sample space of an experiment. They are mutually exclusive and each trial yields exactly one outcome. While individual outcomes may be of little practical interest, they are grouped into events, which are sets of outcomes satisfying some condition. In finite sample spaces, any subset can be an event, but in uncountably infinite sample spaces, some subsets may be excluded. Outcomes may have probabilities between zero and one; in discrete distributions each outcome has a probability, while in continuous distributions individual outcomes have zero probability. Some distributions mix continuous and discrete outcomes, where discrete outcomes are called atoms. Under the measure-theoretic definition, the probability of an outcome need not be defined. Equally likely outcomes are assumed in many randomization tools, but not all experiments are easily described by equally likely outcomes.

Did You Know?

• Each possible outcome of a particular experiment is a unique random element.
• Different outcomes are mutually exclusive; only one outcome will occur on each trial.
• In a continuous distribution, individual outcomes all have zero probability.
• Under the measure-theoretic definition of a probability space, the probability of an outcome need not be defined.