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Hypergeometric Distribution

The Hypergeometric Distribution is used like the binomial distribution in that there are TWO outcomes. However, the difference is that the trials are done WITHOUT replacement.

For example when flipping a coin each outcome (head or tail) has the same probability each time. Both heads and tails are outcomes every time on each trial. Therefore the binomial distribution formulas apply.

The following assumptions and rules apply:

  • Discrete distribution.
  • Population, N, is finite and a known value.
  • Two outcomes - call them SUCCESS (S) and FAILURE (F).
  • Number of successes in the population is known, S.
  • Used when sample size,n, is greater than or equal to 5% of N.
  • Trials are done without replacement, dependent.

    Once again, most statistical software can solve for probabilities when given the inputs.

    Probability Formula

    Hypergeometric Distribution Probability Formula

    Example

    Example applying Hypergeometric Distribution







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