Calculating Probabilities

The Problem Statement

Let X be a random variable following a Hypergeometric distribution. All Hypergeometric distributions have three parameters: sample size, population size, and number of successes in the population. For this problem, let X be a sample of size 8 taken from a population of size 39, in which there are 27 successes. An example of where such a distribution may arise is the following:

Statistics, Inc., wants to determine how well the people like its candies. To determine this, they randomly select 8 people from its workforce of 39. (In this workforce, only 27 of those 39 actually like the candies.) Let X be the number of employees surveyed who like the candies.

From the description, we can tell that X has a Hypergeometric distribution. We know this because X is the number of successes in a finite population where subjects cannot be measured more than once.

For those who like pictures, here is a graphic of the probability mass function of X. Note that it has a negative skew (left skew), that its sample space is integers between 0 and 8, inclusive. In other words, S = {0, 1, 2, …, 8}.

The Probability Graphic

Here is the probability function of the Hypergeometric distribution described in the example:

To Calculate

Continuing the candy example, let us determine the probability that exactly 2 people in the survey respond that they like the candies. In symbols, calculate P[X = 2].

Your Answer

Another Hypergeometric Distribution

Would you like to continue working on this topic? If so, click here for another Hypergeometric distribution.

Assistance