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 18 taken from a population of size 47, in which there are 10 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 18 people from its workforce of 47. (In this workforce, only 10 of those 47 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 positive skew (right skew), that its sample space is integers between 0 and 10, inclusive. In other words, S = {0, 1, 2, …, 10}.

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 1 person in the survey respond that they like the candies. In symbols, calculate P[X = 1].

Your Answer

Another Hypergeometric Distribution

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

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