Sample space

Definition

Sample space is the set of all possible outcomes of a probability experiment. It provides a comprehensive list of every potential result that can occur.

5 Must Know Facts For Your Next Test

1. The sample space can be finite or infinite depending on the nature of the experiment.
2. Each outcome in the sample space is known as a sample point.
3. The notation for sample space is often $S$ or $\Omega$.
4. In simple experiments like flipping a coin, the sample space can be easily enumerated (e.g., S = {Heads, Tails}).
5. Understanding the sample space is crucial for calculating probabilities and constructing probability distributions.

Review Questions

• What is a sample space and why is it important in probability?
• How would you represent the sample space for rolling a six-sided die?
• What is the difference between finite and infinite sample spaces?

Related terms

Event:

A subset of the sample space; a specific outcome or group of outcomes.

Probability Distribution:

A mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

Complementary Event: $1 - P(A)$ where $P(A)$ is the probability of event A occurring; represents all outcomes not in event A.