Hypergeometric Distribution Calculator

Your details

Total number of items in the population. Must be a positive integer (e.g. 52 cards in a deck).
Number of items in the population that count as a success (e.g. 13 hearts in a deck).
Number of items drawn from the population without replacement (e.g. 5 cards dealt).
Number of successes observed in the drawn sample (e.g. exactly 2 hearts in your hand).
P(X = k)Likely
0.27428

Probability of observing exactly k successes in the sample

P(X < k)0.632953
P(X <= k)0.907233
P(X > k)0.092767
P(X >= k)0.367047
Mean (mu)1.25
Variance (sigma^2)0.864
Std Dev (sigma)0.9295
P(X = k)0.27428
P(X <= k)0.907233
P(X >= k)0.367047

P(X = 2) = 27.43% with N=52, K=13, n=5.

  • There is a 27.43% chance of drawing exactly 2 successes in a sample of 5 from a population of 52 with 13 successes.
  • On average you would expect 1.25 successes per draw of 5, with a standard deviation of 0.93.
  • The probability of drawing at least 2 successes is 36.70%.

Next stepCompare P(X = 2) with the mean (1.25) to see how close your outcome is to what you would expect on average.

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