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Hypergeometric Distribution During a particular period a post office received 40 service orders for problems with...

Hypergeometric Distribution

During a particular period a post office received 40 service orders for problems with mail, of which 9 were boxes and 4 were envelopes. A sample of 5 of these service orders is to be selected for inclusion in a customer satisfaction survey. Suppose that the 5 are selected in a completely random fashion, so that any particular subset of size 5 has the same chance of being selected as does any other subset. What then is the probability that exactly x (x = 0, 1, 2, 3, 4, or 5) of the selected service orders were for envelopes?

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Answer #1

Let X is a random variable shows the number of envelops out of 5 selected. Here X has hyper geometric distribution with following parameters:

Population size: N = 40

Sample size: n = 5

Number of envelops in population: k = 4

Since number of envelops are only 4 so x can take values 0, 1, 2, 3, and 4.

The probability of selecting 0 envelops is

The probability of selecting 1 envelop is

The probability of selecting 2 envelops is

The probability of selecting 3 envelops is

The probability of selecting 4 envelops is

The probability of selecting 5 envelops is

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