# Definition:Sample Space

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## 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 $\EE$ 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 $\Omega$

## 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