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Outcome

Definition

Let SS be a sample space. An outcome is an element ω∈S\omega\in S representing one possible result of the random experiment.

Interpretation

An outcome is one complete result of the experiment, described at the level of detail that the model records. Each run of the experiment produces exactly one outcome.

The sample space of a die roll with the outcome 4 of one particular roll highlighted.

The figure shows the sample space of a die roll with the realized outcome ω=4\omega=4. The event {2,4,6}\{2,4,6\} occurs because it contains 44; the event {1,2}\{1,2\} does not.

How much detail an outcome carries is a modelling choice: for two coin tosses an outcome can be the ordered pair, such as HTHT, or only the number of heads. For fair coins the four ordered pairs are equally likely, while the three counts are not, since one head arises from both HTHT and THTH.

An outcome ω\omega is an element of SS, while an event is a set of outcomes. Later, a random variable attaches a number to each outcome.

Key Results

  • An outcome is a single element of the sample space.
  • The level of detail in an outcome depends on how the experiment is modelled.
  • Events are collections of outcomes.

Examples

  • For one die roll, the outcome can be the face that appears.
  • For two coin tosses, an outcome can record the ordered pair of heads and tails.
  • For a customer-order experiment, an outcome might include purchase amount, item type, and delivery time.

Prerequisites

Sources

Aliases: sample point, elementary outcome Symbols: element of, omega

Last updated: 20 October 2026 03:02