A production facility employs 10 workers on the day shift, 8 workers on the swin

Question

A production facility employs 10 workers on the day shift, 8 workers on the swing shift, and 6 workers on the graveyard shift. A quality control consultant is to select 3 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 3 workers has the same chance of being selected as does any other group (drawing 3 slips without replacement from among 24). (a) How many selections result in all 3 workers coming from the day shit? selections What is the probability that all 3 selected workers will be from the day shift? (Round your answer to four decimal places.) (b) What is the probability that all 3 selected workers will be from the same shift? (Round your answer to four decimal places.) (d) 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

(D) Consider an event where all the groups i.e. shifts workers are represented. This means from each group exactly one worker is selected. Probability of this = (10*8*6) / 24C3 = 480/2024 = 0.2372

0.2372 is the probability where each group has exactly one representative. Now in order to find the probability such that at least one of the shift is unrepresented, we can take complement of the calculated probability.

Hence required probability = 1- 0.2372 = 0.7628

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