Key Concepts

• A hypergeometric distribution does not consist of Bernoulli trials.
• In a hypergeometric experiment, the probability of “success” is not the same, because sampling is done without replacement, which means each selection is not independent.
• The number of trials in a hypergeometric experiment is fixed.

Glossary

hypergeometric experiment: a statistical experiment with the following properties:

1. You take samples from two groups.
2. You are concerned with a group of interest, called the first group.
3. You sample without replacement from the combined groups.
4. Each pick is not independent, since sampling is without replacement.
5. You are not dealing with Bernoulli Trials.

hypergeometric probability: a discrete random variable $(RV)$ that is characterized by:

1. A fixed number of trials.
2. The probability of success is not the same from trial to trial.

We sample from two groups of items when we are interested in only one group. $X$ is defined as the number of successes out of the total number of items chosen. Notation: $X \sim H(r, b, n)$, where $r =$ the number of items in the group of interest, $b =$ the number of items in the group not of interest, and $n =$ the number of items chosen.