Probability Basics: Sample Spaces and Events

Key vocabulary covering experiments, sample spaces, events, and fundamental set operations used in introductory probability.

Experiment

Any action or process whose outcome is subject to uncertainty (e.g., tossing a coin, rolling a die).

Outcome

A single possible result of an experiment (such as getting Heads when a coin is tossed).

Sample Space (S)

The set of all possible outcomes of an experiment.

Event

A subset of the sample space; it contains one or more outcomes.

Simple Event

An event consisting of exactly one outcome from the sample space.

Compound Event

An event containing two or more outcomes from the sample space.

Union of Events (A ∪ B)

The set of outcomes that belong to event A, event B, or both.

Intersection of Events (A ∩ B)

The set of outcomes common to both event A and event B.

Complement of an Event (Aᶜ or A′)

All outcomes in the sample space that are not in event A.

Disjoint / Mutually Exclusive Events

Events that share no common outcomes; their intersection is empty.

Venn Diagram

A visual tool using overlapping circles to illustrate relationships among sets or events.

Infinite Sample Space

A sample space that contains infinitely many outcomes (e.g., sequential battery tests until success).

Subset

A set whose elements all belong to another set; in probability, every event is a subset of the sample space.

Ordered‐Pair Sample Space

A sample space whose outcomes are ordered pairs, such as (3,5) for pumps in use at two gas stations.

Success–Failure Experiment

An experiment where each trial results in either success or failure, often continued until the first success.