<span>When you are sampling from a small finite lot, the hypergeometric distribution applies. The binomial is a poor approximation in this case. The general equation for the hypergeometric where aCx means the number of combinations of a items selected x at-a-time.: P(x) =[(aCx)(N-aCn-x)]/NCn Where N is the lot size = 20 a is the number of defectives in the lot = 3. x is the number of defectives in the sample. n is the sample size = 2. A. The probability that the first item is defective is P(x=1) = [(3C1)(17C1)]/(20C2) = (3)(17)/190 = 0.268 The probability that the second item is defective is P(x = 1) = [(2C1)(17C1)]/(19C2) = (2)(17)/171 = 0.199. So the total probability is (0.268)(0.199) = 0.0532 B. The probability that the first item is good is: P(x = 0) = (3C0)(16C2)]/20C2 = (1)(120)/190 = 0.632 The probability that the second item is defective is P(x = 0) =[(3C0)(16C2)]/19C2 = (1)(120)/171 = 0.670. The total probability is 0.632(0.670) = 0.4234</span>
