Sample space

The sample space is the set of all possible outcomes of a random experiment, the starting point for defining events and assigning probabilities.

ByHoang TruongUpdated July 11, 2026

See it move

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A firm assigns each order to one of 3 suppliers and one of 4 delivery methods. Because the two choices are independent, the sample space is every supplier-method pair possible, and its size is found by multiplying the option counts: 3 × 4 = 12 possible outcomes, from (A, air) through to (C, road).

Where it fits

TopicProbability & DistributionsCoreSubjectData Analysis & StatisticsCore

The formula

LaTeX

|S| = n_1 \times n_2 \times \cdots \times n_k

Variables

$∣ S ∣$: Number of outcomes in the sample space
$n_{1}$: Number of possible outcomes at stage 1
$n_{2}$: Number of possible outcomes at stage 2

Gives the number of outcomes in a sample space built from several independent stages, by multiplying the option counts at each stage.

Check yourself

PracticeCORE

A customer selects one of 5 product colours and one of 3 sizes. How many outcomes (colour, size) are in the sample space?

Select an answer to check your understanding.