HYPERGEOMETRIC DISTRIBUTION ASSIGNMENT HELP

This is a special case of the Binomial distribution only that it is without replacement.

Properties

The following are characteristics of hypergeometric experiments:

1. Samples are taken from two groups.
2. The interest is in the first group.
3. Sampling from the combined groups is done without replacement.
4. Each sample draw is not independent. This is to say the probability of each sample pick is dependent on the previous sample pick(s).
5. It is important to bear in mind that these are not Bernoulli Trials.

Characteristics

1. The hypergeometric distribution consists of a finite number of trials.
2. In each trial, the probability of success differs.

Example

Let’s say that you have $1,100 in your pocket. Furthermore, $800 is in 100-dollar bills and the rest is in 50-dollar bills.You randomly draw 5 bills without replacing. Find the probability that you will draw exactly 3 50-dollar bills.

Answer

The number of 100-dollar bills is $800/$100 = 8
The number of 50-dollar bills is $(1100-800)/$50=$300/$50 = 6
In total, you have 8 + 6 = 14 bills.
Hence our parameters take the following values;
N = 14; Population size
k = 6; Number of successes in the population
n = 5; Sample size
x = 3; Desired number of successes in the sample
We now substitute the above parameters into the hypergeometric formula as shown below;
P = [ ₆C₃ ] [ _14-6C_5-3 ] / [ ₁₄C₅ ]
P = (20*28)/2002
P = 0.2797
We find that the probability of drawing exactly 3 50-dollar bills from your pocket given the above parameters is 0.2797.