Sample space

Definition

A sample space is the set of all possible outcomes of a probability experiment. It is denoted by $S$ and serves as the foundation for defining events in probability theory.

5 Must Know Facts For Your Next Test

1. The sample space must include every possible outcome of the experiment without any duplication.
2. For discrete random variables, the sample space can be finite or countably infinite.
3. For continuous random variables, the sample space is often an interval or a collection of intervals on the real number line.
4. The probability of the entire sample space $P(S)$ is always equal to 1.
5. Events are subsets of the sample space, and their probabilities are calculated based on how they relate to the entire sample space.

Review Questions

• What is a sample space and how is it denoted?
• Why must the probability of the entire sample space be equal to 1?
• How do you determine if an event belongs to a given sample space?

Related terms

Event: A subset of a sample space that represents one or more outcomes.

Outcome: A single result from a probability experiment belonging to the sample space.

$P(E)$: $P(E)$ denotes the probability of event $E$, which is calculated as $\frac{n(E)}{n(S)}$ for equally likely outcomes.