Hypergeometric distribution calculator
Example: the chance of exactly one ace in 5 cards from 52. Enter the population, the wanted items in it and the number drawn.
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How to use it
- Enter population size n, wanted items in population k, number drawn n and wanted items drawn k.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
P(X = k) = C(K, k) × C(N - K, n - k) ÷ C(N, n), with population N, K wanted items in it and n draws. Mean = n × K ÷ N.
Example
Inputs: Population size N = 52, Wanted items in population K = 4, Number drawn n = 5, Wanted items drawn k = 1. Result: P(X = k): 0.2994736356; P(X < k): 0.6588419983; P(X ≤ k): 0.9583156339.
Limits and caveats
- For draws without replacement from a population with two kinds: wanted and not wanted.
- Population up to 100000.
Questions about this tool
When should I use it instead of the binomial?
When items are not put back, so the chance changes with each draw, as with cards or sampling a small batch.
What is the chance of at least one ace in 5 cards?
P(X ≥ 1) ≈ 34.12%, shown for N = 52, K = 4, n = 5 and k = 1.
Can it be used for batch quality checks?
Yes, put the batch size in N, the defective count in K and the sample size in n.