Hypergeometric Calculator — Formula
## 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.
### 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.
Esempio Risolto
A deck has 50 cards, 10 are red. Draw 5 cards without replacement. What is the probability of exactly 2 red cards?
- C(10,2) = 45
- C(40,3) = 9880
- C(50,5) = 2118760
- P(X=2) = (45 * 9880) / 2118760
- = 444600 / 2118760 ≈ 0.20985