A production facility employs 20 workers on the day shift, 15 workers on the swi

Question

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). How many selections result in all 6 workers coming from the day shift? selections What is the probability that all 6 selected workers will be from the day shift? (Round your answer to four decimal places.) What is the probability that all 6 selected workers will be from the same shift? (Round your answer to four decimal places.) What is the probability that at least two different shifts will be represented among the selected workers? (Round your answer to four decimal places.) What is the probability that at least one of the shifts will be unrepresented in the sample of workers? (Round your answer to four decimal places.)

Explanation / Answer

a)No of selections that result in all 6 workers coming from day shift = 20C6 = 38760

b)Total no of selctions i.e 6 from 45 =  45C6 = 8145060

probablity that all 6 workers will be from day shift = 38760/8145060 = 0.00475

c)No of ways in which only one group represent all the 6 selections . = 20C6 +15C6 +10C6 = 38760+5005+210 = 43975

Probability that only one group represent all the 6 selections = 43975 /8145060 = 0.0054

Probabilty that atleast two groups will represent among selected workers = 1 -Probability that only one group represent all the 6 selections = 1- 0.0054 = 0.9946

d)No of ways in which atlast one shift is unrepresented = (20+15)C6+(20+10)C6+(10+15)C6 - (20C6 +15C6 +10C6) = 1623160+593775+177100 - 43975= 2350060

Probablity that aleast one group is unrepresented = 2350060/8145060 = 0.2885

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