A company that produces fine crystal knows from experience that 10% of its goblets have cosmetic flaws and must be classified as “seconds.” a.? ?Among six randomly selected goblets, how likely is it that only one is a second? b. ?Among six randomly selected goblets, what is the probability that at least two are seconds? c. ?If goblets are examined one by one, what is the probability that at most five must be selected to find four that are not seconds?

Answer: Step 1 of 3 a. Among six randomly selected goblets, how likely is it that only one is a second p = 10% p = 0.1 and n = 6 1 6 1 P(X = 1) = 6C 10.1) (1 0.1) = 6 × 0.1 × 0.5904 = 0.3542 Therefore, the probability one of 6 has a flaw is 0.3542. Step 2 of 3 b. Among six randomly selected goblets, we need to find the probability that at least two are seconds p = 10% p = 0.1 and n = 6 P(X 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) Using Excel function, “=BINOMDIST(x,n,p,false)” x P(x) 2 0.098415 3 0.01458 4 0.001215 5 0.000054 6 0.000001 Sum 0.114265 Therefore, P(X 2) = 0.1143