Marginal probability

Marginal probability is the probability of one event alone, found by summing the relevant row or column of a joint probability table across all outcomes of the other variable.

ByHoang TruongUpdated July 11, 2026

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Of 200 employees, 40 are Sales/remote, 60 Sales/office, 50 Operations/remote and 50 Operations/office. The marginal probability of Sales sums the whole Sales row: 40/200 + 60/200 = 0.20 + 0.30 = 0.50, ignoring work preference entirely. Marginal probability always divides by the grand total, unlike conditional probability, which divides by one row's own total.

Where it fits

TopicProbability & DistributionsCoreSubjectData Analysis & StatisticsCore

The formula

LaTeX

P(A_i) = \sum_{j} P(A_i \cap B_j)

Variables

$P (A_{i})$: Marginal probability of outcome A_i
$P (A_{i} \cap B_{j})$: Joint probability of A_i occurring together with B_j

Gives the marginal probability of one outcome by summing its joint probabilities across every outcome of the other variable in a joint probability table.

Check yourself

PracticeCORE

A retailer classifies 120 customers by region and payment method: North-card 30, North-cash 10, South-card 50, South-cash 30. What is the marginal probability that a randomly chosen customer paid by cash?

Select an answer to check your understanding.