Statistics

Hypergeometric Distribution Calculator

Find the probability of k successes when sampling without replacement.

Calculated Output

P(X = k) 0.2995

Formula: P = C(K,k)·C(N−K,n−k) ÷ C(N,n)

Step-by-Step Breakdown

1. Values used:

2. Population size = 52

3. Successes in population = 4

4. Sample size = 5

5. Successes drawn = 1

7. P(X = k) = 0.2995

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The math behind it

P(X = k) = C(K,k)·C(N−K,n−k) ÷ C(N,n), for a population of N with K successes.

Drawing 5 cards, P(exactly 1 ace) ≈ 0.299.

Hypergeometric vs binomial?

Binomial samples with replacement; hypergeometric without.