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 4 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 4 workers has the same chance of being selected as does any other group (drawing 4 slips without replacement from among 24) (a) How many selections result in all 4 workers coming from the day shift? selections What is the probability that all 4 selected workers will be from the day shift? (Round your answer to four decimal places.) (b) What is the probability that all 4 selected workers will be from the same shift? (Round your answer to four decimal places.) (C) What is the probability that at least two different shifts will be represented among the selected workers? (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

10 day shift workers
8 swing shift
6 graveyard shift

There are total 24 workers, and 4 workers from them can be randomly selected in 24C4 ways = 10626

(a)
4 workers can be selected from day shift in 10C4 ways
= 210 selections

Required probabiltiy = 210/10626 = 0.01976

(b)
Same shift selections can be done in 10C4 + 8C4 + 6C4 ways i.e. 295 selections

Required probability = 295/10626 = 0.0278

(c)
Probability that at least two different shifts workers can be selected = 1 - 0.0278 = 0.9722

(d)
Lets consider none of the shift is unrepresented, possible selections are
10C2*8C1*6C1 + 10C1*8C2*6C1 + 10C1*8C1*6C2 = 5040

Required probability = 1 - 5040/10626 = 1 - 0.4743 = 0.5257

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