A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10 workers on the graveyard shift. A quality control consultant is to select 6 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 6 workers has the same chance of being selected as does any other group (drawing 6 slips without replacement from among 45). a. ?How many selections result in all 6 workers coming from the day shift? What is the probability that all 6 selected workers will be from the day shift? b.? ?What is the probability that all 6 selected workers will be from the same shift? c. ?What is the probability that at least two different shifts will be represented among the selected workers? d. ?What is the probability that at least one of the shifts will be unrepresented in the sample of workers?

Answer: Step 1: A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10 workers on the graveyard shift. Suppose 6 workers are to be selected from the total (20+15+10) = 45 workers for in-depth interviews. 45 The total number of ways to select 6 members for a group of 45 members is c6. Step 2: a). We have to find how many selections result in all 6 workers coming from the day shift. The probability that all 6 selected workers will be the day shift is c60 P(the day shift) = 45 =0.0047 c6 Step 3: b). To find the probability that all 6 selected workers will be from the same shift. The probability that all 6 selected workers will be from the same shift is 20 15 10 c6 c6 c6 P(the same shift) = c 45 + c45 + c45 6 6 6 = 0.0047+0.0006+ 0 = 0.0053.