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Probability · Quick Reference
Sample Space Cheat Sheet
In one line: the sample space is the complete list of every possible outcome of an experiment — the foundation everything else in probability builds on.
Key Ideas
1Sample Space (S). The set of all possible outcomes of a random experiment. Example: rolling a die gives S = {1,2,3,4,5,6}.
2Outcome. A single possible result of an experiment, such as rolling a 4.
3Finite 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).
4Equally Likely Outcomes. When every outcome in S has the same chance of occurring, such as each face of a fair die.
5Listing Sample Spaces for Combined Experiments. For two experiments done together (like flipping a coin and rolling a die), list every ordered pairing of outcomes.
Worked Examples
Write the sample space for flipping a single coin.
S = {H, T}
Write the sample space for rolling a standard six-sided die.
S = {1, 2, 3, 4, 5, 6}
Write the sample space for flipping a coin and rolling a die together.
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)}
Formulas
n(S) = total number of outcomes in the sample space
Practice Yourself
How many outcomes are in the sample space of rolling one die?
6
Write the sample space for drawing a card's suit (ignore rank).
S = {Hearts, Diamonds, Clubs, Spades}
How many outcomes result from flipping two coins?
4