Suppose a researcher goes to a small college with 200 faculty, 12 of which have blood type O-negative. She obtains a simple random sample of n = 20 of the faculty. Let the random variable X represent the number of faculty in the sample of size n = 20 that have blood type O-negative.

(a) What is the probability that three of the faculty have blood type O-negative?

(b) What is the probability that at least one of the faculty has blood type O-negative?

Approach This is a hypergeometric experiment with N = 200, n = 20, and k = 12. The possible values of the random variable X are x = 0, 1, 2,c, 12. (Our sample cannot have more than k = 12 faculty with blood type O-negative.) Use Formula (1) to compute the probabilities.