Free Hypergeometric Calculator
Calculate the probability of drawing exactly k successes in n draws from a finite population without replacement.
P(X = k)
0.20983972
P(X = k) vs Population Size (N)
How to Calculate Hypergeometric Probability
Formula
P(X = k) = C(K,k) * C(N-K, n-k) / C(N, n)
The hypergeometric distribution models sampling without replacement from a finite population of N items containing K successes. It answers: if you draw n items, what is the probability of getting exactly k successes? Unlike the binomial, the probability changes with each draw.
Example Calculation
A deck has 50 cards, 10 are red. Draw 5 cards without replacement. What is the probability of exactly 2 red cards?
- 01C(10,2) = 45
- 02C(40,3) = 9880
- 03C(50,5) = 2118760
- 04P(X=2) = (45 * 9880) / 2118760
- 05= 444600 / 2118760 ≈ 0.20985
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