Hypergeometric Distribution Calculator

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Introduction

Hypergeometric Distribution Calculator — Compute probability of k successes drawn without replacement. Enter Population size (N), Successes in population (K), Sample size (n), Successes in sample (k) to get an instant, accurate result.

Formula

PMF: P(X=k) = [C(K,k) × C(N−K, n−k)] / C(N,n), the probability of exactly k successes when drawing n items without replacement from a population of N containing K successes.

Step-by-step

Enter the Population size (N).
Enter the Successes in population (K).
Enter the Sample size (n).
Enter the Successes in sample (k).
Click Calculate to see your result instantly.

Real-world example

Example: With Population size (N) = 20, Successes in population (K) = 7, Sample size (n) = 5, Successes in sample (k) = 2, the Hypergeometric Distribution Calculator gives Probability: 0.3874.

Frequently Asked Questions

How is this different from the binomial distribution?

Binomial assumes each draw is independent with a constant success probability (sampling with replacement); hypergeometric assumes sampling without replacement, so the probability changes with each draw.

What is a real-world example?

Calculating the probability of drawing a specific number of winning cards from a deck, or defective items from a batch, when items aren't put back after being drawn.

What inputs does the Hypergeometric Distribution Calculator need?

You'll need to provide: Population size (N), Successes in population (K), Sample size (n), Successes in sample (k). All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.

How accurate is the Hypergeometric Distribution Calculator?

The Hypergeometric Distribution Calculator applies the formula exactly as calculated — PMF: P(X=k) = [C(K,k) × C(N−K, n−k)] / C(N,n), the probability of exactly k successes when drawing n items without replacement from a population of N containing K successes. — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.

Is the Hypergeometric Distribution Calculator free to use?

Yes, the Hypergeometric Distribution Calculator is completely free, requires no signup, and runs instantly in your browser.

About the Hypergeometric Distribution Calculator

The Hypergeometric Distribution Calculator uses a real, verifiable formula — PMF: P(X=k) = [C(K,k) × C(N−K, n−k)] / C(N,n), the probability of exactly k successes when drawing n items without replacement from a population of N containing K successes. — so results are accurate every time, not an approximation.