Hypergeometric Distribution Calculator
Evaluate probabilities of drawing k successes in n draws without replacement from a finite population.
P(X = k): 0.133032
P(X ≤ k): 0.953975
P(X ≥ k): 0.046025
Mean: 2.400
Variance: 1.489
How to Use This Calculator
- Define total population size, N.
- Specify how many of those are successes, K.
- Enter the number of draws n (without replacement).
- Provide k, the observed number of successes in your sample.
- Review point and cumulative probabilities along with mean and variance.
Formula
P(X = k) = [C(K, k) · C(N − K, n − k)] / C(N, n)
Mean = n · K / N
Variance = n · K · (N − K) · (N − n) / [N² · (N − 1)]
The hypergeometric distribution models sampling without replacement. When sampling with replacement, the binomial distribution applies instead.
Frequently Asked Questions
When should I use the hypergeometric distribution?
Use it when sampling without replacement from a finite population containing successes and failures.
What happens when N is large?
As N grows (with fixed n), the hypergeometric distribution approaches the binomial distribution.
Can k exceed n?
No. k must lie between max(0, n + K − N) and min(n, K). Outside this range, the probability is zero.