HyperGeo is an Hypergeometric calculator that computes single and cumulative hypergeometric probabilities.

A Hypergeometric distribution refers to the probabilities of choosing a set of items from a larger population, all having a certain property.

For example:

• Choosing 7 cards from a deck of 52 playing cards and then calculating the probabilities of having 0, 1, 2, 3, 4, 5, 6 or 7 red cards, or the cumulative probability of having up to, say, 4 red cards.

• From a batch of 100,000 manufactured goods, 1,200 of which are known to be faulty, calculating the probability that if you purchase 10 items, none of them will be faulty.

• Choosing 6 numbers in a 49-ball lottery, and calculating the probabilties of having 0, 1, 2, 3, 4, 5 or 6 winning numbers.

All of these types of problem go beyond trivial probability calculations due to the fact that as individual samples are removed from the population, the probability of having another 'success' changes. e.g. after drawing one red card from a pack the probability is no longer 26/52 but is now 25/51.

HyperGeo uses the conventions:
N = total population (e.g. 52 cards)
m = successes in population (26 red cards)
n = sample size (e.g. taking 7 cards)
k = succeses in sample (e.g. 4 red)

Mean and variance are shown along with the probabilities. Large numbers up to 4.294 billion are supported.