What is hypergeometric distribution?

hypergeometric distribution describes the likelihood of certain events when the sequence of items is drawn from a solid set such as selecting playing cards from the package. The key characteristic of the event after the distribution of hypergeometric probability is that the items are not replaced between draws. After a specific object has been selected, it cannot be re -selecting. This feature is most important when working with small populations.

Quality evaluation auditors use hypergeometric distribution to analyze the number of defective products in a given group. The products are canceled after testing because there is no reason to test the same product twice. The selection is therefore made without compensation.

Poker probabilities are calculated using hypergeometric distribution because the cards are not shuffled back to the deck in that hand. Initially, for example, one quarter of the standard deck cards are spades, but the likelihood of two -cards and finding that both of them are spades, not 1/4 * 1/4 = 1/16. After receiving PRThere are fewer spades left on board, so the likelihood of another spade is to be distributed is only 12/51. The probability that two cards will be distributed and found that the spades are 1/4 * 12/51 = 1/17.

objects are not replaced between draws, so the likelihood of extreme scenarios is reduced for hypergeometric distribution. One may compare that red or black cards from a standard package will be distributed after the coin rolling. The fair coin lands in half the "head" and half of the cards in the standard deck is black. Yet the probability of obtaining five consecutive heads when rolling the coin is more than the likelihood of a five card to be distributed and found that all black cards are. The likelihood of five consecutive heads is 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32, or about 3 percent, the cost of five black cards is 26/52 * 25/51 * 24/50 * 23/49 * 22/48 = 253/9996,or about 2.5 percent.

sampling without compensation reduces the likelihood of extreme cases, but does not affect the arithmetic average of distribution. The average number of heads was expected to turn one over the coin five times, is 2.5, which is equal to the average number of black cards expected in five cards. Just as it is very unlikely that all five cards are black, it is also unlikely that none of them. This is described in the mathematical language by reducing the scattering without affecting the expected distribution value.