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- Statistics - Discussion
Statistics - Hypergeometric Distribution
A hypergeometric random variable is the number of successes that result from a hypergeometric experiment. The probability distribution of a hypergeometric random variable is called a hypergeometric distribution.
Hypergeometric distribution is defined and given by the following probability function:
Formula
${h(x;N,n,K) = \frac{[C(k,x)][C(N-k,n-x)]}{C(N,n)}}$
Where −
${N}$ = items in the population
${k}$ = successes in the population.
${n}$ = items in the random sample drawn from that population.
${x}$ = successes in the random sample.
Example
Problem Statement:
Suppose we randomly select 5 cards without replacement from an ordinary deck of playing cards. What is the probability of getting exactly 2 red cards (i.e., hearts or diamonds)?
Solution:
This is a hypergeometric experiment in which we know the following:
N = 52; since there are 52 cards in a deck.
k = 26; since there are 26 red cards in a deck.
n = 5; since we randomly select 5 cards from the deck.
x = 2; since 2 of the cards we select are red.
We plug these values into the hypergeometric formula as follows:
Thus, the probability of randomly selecting 2 red cards is 0.32513.