01 Key Concepts
Sample Space (S)
The set of all possible outcomes of a random experiment. Example: rolling a die gives S = {1,2,3,4,5,6}.
Outcome
A single possible result of an experiment, such as rolling a 4.
Finite vs. Infinite Sample Spaces
A finite sample space has a countable number of outcomes (a coin flip); an infinite one does not (measuring exact time until a lightbulb fails).
Equally Likely Outcomes
When every outcome in S has the same chance of occurring, such as each face of a fair die.
Listing Sample Spaces for Combined Experiments
For two experiments done together (like flipping a coin and rolling a die), list every ordered pairing of outcomes.
02 Key Formulas
- n(S) = total number of outcomes in the sample space
03 Solved Examples
Example 1 Write the sample space for flipping a single coin.
- A coin has exactly two possible outcomes: heads or tails.
Answer: S = {H, T}
Example 2 Write the sample space for rolling a standard six-sided die.
- A standard die has six faces, numbered 1 through 6.
Answer: S = {1, 2, 3, 4, 5, 6}
Example 3 Write the sample space for flipping a coin and rolling a die together.
- Pair each coin outcome (H, T) with each die outcome (1-6).
- This gives 2 x 6 = 12 total ordered pairs.
Answer: S = {(H,1),(H,2),(H,3),(H,4),(H,5),(H,6),(T,1),(T,2),(T,3),(T,4),(T,5),(T,6)}
04 Practice Questions
1How many outcomes are in the sample space of rolling one die?
6
2Write the sample space for drawing a card's suit (ignore rank).
S = {Hearts, Diamonds, Clubs, Spades}
3How many outcomes result from flipping two coins?
4
4Write the sample space for flipping two coins.
S = {HH, HT, TH, TT}
5Is 'time until a phone battery dies' a finite or infinite sample space?
Infinite
📄 Sample Space — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.