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

solution=

nCr is the number of ways of taking r objects from a set of n.

a. the probability you need is 10C4 / 24C4 =210/10626=.0.0198

the numerator is the answer for the number of selections

.
b. answer: [10C4 + 8C4 + 6C4] / 24C4 =0.0278

c. the answer is the complement of b.
1 - "answer of b". ... it can also be written as1- [10C4 + 8C4 + 6C4] / 24C4=0.9722

d. its complement is the event where all shifts are represented. to get that choose one worker from each shift.
then randomly choose the others from the whole group.
10*8*6*22C2 / 24C4 ... this is the representation of the complement.
so the answer is
[24C4 - 10*8*6*22C2] / 24C4 =9.4348

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