Hypergeometric Distribution Calculator
Calculate probability when sampling without replacement.
Hypergeometric Formula
P(X=k) = C(K,k) × C(N−K,n−k) / C(N,n). It applies to sampling without replacement from a finite population.
Understanding the Hypergeometric Distribution
The hypergeometric distribution models successes in draws made without replacement from a finite population.
Hypergeometric Example
If a box contains 20 items, 5 defective, and 4 are sampled without replacement, the calculator can estimate the probability of finding a chosen number of defective items.
When to Use It
Use this model when the population is finite and each draw changes the composition of what remains.
Frequently Asked Questions
How is it different from binomial?
Binomial assumes independent trials, while hypergeometric sampling is without replacement.
Can sample size exceed population size?
No.
Does order matter?
No, the model focuses on counts of successes.
When to Use the Hypergeometric Distribution
The hypergeometric distribution calculates probabilities when items are sampled without replacement from a finite population containing successes and failures. Because selected items are not returned to the population, the probability changes from one draw to the next.
Typical inputs are population size, number of success items in the population, sample size and the desired number of successes. For example, it can estimate the chance of finding a certain number of defective items when inspecting a batch without replacement. All counts should be whole numbers, the sample cannot exceed the population, and the number of successes must be feasible.
This differs from the binomial model, which generally assumes independent trials with a constant success probability. When sampling without replacement represents a meaningful fraction of a finite population, the hypergeometric model is often the better choice.
Methodology, Assumptions and Interpretation
The hypergeometric distribution models successes when sampling without replacement from a finite population. Unlike the binomial model, draws are dependent because each selection changes the remaining population composition.