Hypergeometric Calculator

Calculate the probability of drawing exactly k successes in n draws from a finite population without replacement.

P(X = k)

0.20983972

Expected Value1.0000
Variance0.7347

P(X = k) vs Population Size (N)

सूत्र देखें →

सूत्र

## 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.

हल किया गया उदाहरण

A deck has 50 cards, 10 are red. Draw 5 cards without replacement. What is the probability of exactly 2 red cards?

  1. 01C(10,2) = 45
  2. 02C(40,3) = 9880
  3. 03C(50,5) = 2118760
  4. 04P(X=2) = (45 * 9880) / 2118760
  5. 05= 444600 / 2118760 ≈ 0.20985