Mail rooms contaminated with anthrax. In the fall of 2001, there was a highly publicized o...

Mail rooms contaminated with anthrax. In the fall of 2001, there was a highly publicized outbreak of anthrax cases among U.S. Postal Service workers. In Chance (Spring 2002), research statisticians discussed the problem of sampling mail rooms for the presence of anthrax spores. Let x equal the number of mail rooms contaminated with anthrax spores in a random sample of n mail rooms selected from a population of N mail rooms. The researchers showed that the probability distribution for x is given by the formula

where k is the number of contaminated mail rooms in the population. (This probability distribution is known as the hypergeometric distribution.) Suppose N = 100, n = 3, and k = 20.

a. Find p(0).

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b. Find p(1).

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c. Find p(2).

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d. Find p(3).