Pre-Algebra
Probability (introductory)
Sample spaces (lists, tables, tree diagrams)
20 practice questions
0 video lessons
Theory + worked examples
Sample Spaces (Lists, Tables, Tree Diagrams)
California Pre-Algebra • Standard 7.SP.8 • Probability
Sample Spaces (Lists, Tables, Tree Diagrams) is a topic in Probability in the California Common Core State Standards. It is aligned to Standard 7.SP.8, which requires students to represent sample spaces with lists, tables, and tree diagrams.
A sample space lists all possible outcomes; lists, tables, and tree diagrams organize them.
Theory
A sample space is the set of all possible outcomes. It can be shown as a list, table, or tree diagram.
Counting principle: multiply the choices at each step for the total.
A tree diagram for two coins.
Ways to show a sample space.
Counting principle:
\[\text{total outcomes}=n_1\cdot n_2\cdots\]
Each branch of a tree is one outcome.
How to build a sample space
- List outcomes for each step.
- Use a tree or table to combine them.
- Multiply choices for the total count.
- Read probabilities from the space.
Example 1 — Count outcomes
How many outcomes for flipping two coins?
Solution
\(2\times2\).
| \(2\cdot2\) | \(=\) | \(4\) |
Example 2 — List them
List the sample space for two coins.
Solution
Use a tree or list.
| \(HH,\ HT,\ TH,\ TT\) |
Example 3 — Counting principle
A meal has \(3\) mains and \(2\) drinks. How many combos?
Solution
Multiply.
| \(3\cdot2\) | \(=\) | \(6\) |
Example 4 — Probability from space
Find \(P(HH)\) for two coins.
Solution
One of four.
| \(P(HH)\) | \(=\) | \(\dfrac{1}{4}\) |
Common pitfalls
Include every outcome exactly once.
Multiply the choices, don't add.
Order can matter (HT vs TH).
Frequently asked questions
What is a sample space?
The set of all possible outcomes.
How do I show one?
A list, table, or tree diagram.
What is the counting principle?
Multiply the choices at each step.
How many outcomes for two coins?
\(4\).
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Probability of compound events
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Comparing two populations informally
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