Definition:Sample Space

Definition

Let $\EE$ be an experiment.

The sample space of $\EE$ is usually denoted $\Omega$ (Greek capital omega), and is defined as the set of all possible outcomes of $\EE$.

Discrete Sample Space

If $\Omega$ is a countable set, whether finite or infinite, then it is known as a discrete sample space.

Also denoted as

Some sources denote the sample space of an experiment $\EE$ as $S$.

Examples

Throwing a 6-Sided Die

Let $\EE$ be the experiment of throwing a standard $6$-sided die.

The sample space of $\EE$ is $\Omega = \set {1, 2, 3, 4, 5, 6}$.

Also see

• Definition:Elementary Event or Definition:Sample Point: a typical element of $\Omega$

• Results about sample spaces can be found here.

Sources

• 1965: A.M. Arthurs: Probability Theory ... (previous) ... (next): Chapter $2$: Probability and Discrete Sample Spaces: $2.2$ Sample spaces and events
• 1986: Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction ... (previous) ... (next): $1$: Events and probabilities: $1.2$: Outcomes and events