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All courses Geometry · S-CP.1 40 of 57
Describe events as subsets of a sample space using unions, intersections, and complements.

List the sample space of a finite experiment

Problem
List the complete sample space for flipping \(\text{one}~\text{coin}\) and spinning a spinner labeled \(1,~2,~\text{and}~3\). Pair each coin result with every spinner result.
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Hint

List all coin outcomes and pair each one with each spinner result.

A sample space contains every complete outcome of the experiment. Here, each outcome needs both a coin result and a spinner number.

Solution walkthrough

01

List each component space

\[\text{coin}={H,T};~\text{spinner}={1,2,3}\]

The coin has two results and the spinner has three.

02

Pair H with every spinner value

\[H_{1},H_{2},H_{3}\]

Each compound outcome records one result from each experiment.

03

Pair T with every spinner value

\[T_{1},T_{2},T_{3}\]

This completes the second coin-result row.

04

Check completeness

\[2*3=6~\text{distinct}~\text{outcomes}\]

The multiplication principle confirms no pair is missing or duplicated.

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Another way

  1. Use a two-by-three table and read all six cells.

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Common mistake

Do not list H, T, 1, 2, and 3 separately; each outcome must contain both results.

Solution walkthrough video