# Definition and Examples of a Sample Space in Statistics

The collection of all possible outcomes of a probability experiment forms a set that is known as the sample space.

Probability concerns itself with random phenomena or probability experiments. These experiments are all different in nature and can concern things as diverse as rolling dice or flipping coins. The common thread that runs throughout these probability experiments is that there are observable outcomes. The outcome occurs randomly and is unknown prior to conducting our experiment.

In this set theory formulation of probability, the sample space for a problem corresponds to an important set. Since the sample space contains every outcome that is possible, it forms a set of everything that we can consider. So the sample space becomes the universal set in use for a particular probability experiment.

## Common Sample Spaces

Sample spaces abound and are infinite in number. But there are a few that are frequently used for examples in an introductory statistics or probability course. Below are the experiments and their corresponding sample spaces:

• For the experiment of flipping a coin, the sample space is {Heads, Tails}. There are two elements in this sample space.
• For the experiment of flipping two coins, the sample space is {(Heads, Heads), (Heads, Tails), (Tails, Heads), (Tails, Tails) }. This sample space has four elements.