Chapter 4.2, Problem 4.31ACI

Mail rooms contaminated with anthrax. During autumn 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 mailrooms selected from a population of N mail rooms. The researchers showed that the probability distribution for x is given by the formula

     $p(x)=\frac{\left(\begin{array}{c}k\\ x\end{array}\right)\left(\begin{array}{c}N-k\\ n-x\end{array}\right)}{\left(\begin{array}{c}N\\ n\end{array}\right)}$

where k is the number of contaminated mail rooms in the population. (In Section 4.4 we identify this probability distribution as the hypergeometric distribution.) Suppose N = 100, n = 3, and k = 20.

1. a. Find p(0).
2. b. Find p(1).
3. c. Find p(2).
4. d. Find p(3).