# Hypergeometric distribution

### Hypergeometric distribution

#### Lessons

N: population size
m: number of successes in the population
n: sample size
x: number of successes in the sample

P(x): probability of getting x successes (out of a sample of n)
$P(x)=\frac{(_mc_x)(_{N-m}C_{n-x})}{_NC_n}$
• 1.
What is Hypergeometric Distribution?

• 2.
Identifying Hypergeometric Distributions
Identify which of the following experiments below are Hypergeometric distributions?

i.
Negative Binomial – A 12 sided die (dodecahedra) is rolled until a 10 comes up two times. What is the probability that this will take 6 rolls?
ii.
Binomial – An urn contains 5 white balls and 10 black balls. If 2 balls are drawn with replacement what is the probability that one of them will be white?
iii. Hypergeometric - A bag contains 8 coins, 6 of which are gold galleons and the other 2 are silver sickles. If 3 coins are drawn without replacement what is the probability that 2 of them will be gold galleons?

• 3.
Determining the Hypergeometric Distribution
A bag contains 8 coins, 6 of which are gold galleons and the other 2 are silver sickles. If 3 coins are drawn without replacement what is the probability that 2 of them will be gold galleons?

• 4.
Determining the Cumulative Hypergeometric Distribution
Ben is a sommelier who purchases wine for a restaurant. He purchases fine wines in batches of 15 bottles. Ben has devised a method of testing the bottles to see whether they are bad or not, but this method takes some time, so he will only test 5 bottles of wine. If Ben receives a specific batch that contains 2 bad bottles of wine, what is the probability that Ben will find at least one of them?