# 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 $\EE$ 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 $\Omega = \set {1, 2, 3, 4, 5, 6}$.