A production facility employs 10 workers on the day shift, 8 workers on the swin
ID: 3276266 • Letter: A
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.)
__________
4 praduction facility amploys 10 workers an tha day shift, 8 workers an the swing shift, and G workers an tha gravayard shift. A quality control consultant is to saloct 4 of thase workars for in-dapth interviaws. Suppose the sclection is made in such a way that any particular group of4 workers has the satrie chane f being selected as does ary other group drawing 4 slips without replacerent from aong 24) a) How many selections result in all 4 workers coming from the day shirt? 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 sclacted warkers will be from tha same shift? (Round your answer to four dacimal placas (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 wil be unrepresented in the sample of workers? (Round your answer to tour decimal places.)Explanation / Answer
Four workers can be randomly selected from 24 in 24C4 = 10626 ways
(a)
If consultant all selected 4 workers from day shift, this can be done in 10C4 ways i.e. 210 selections
the probability that all 4 selected workers will be from the day shift = 210/106026 = 0.0198
(b)
Probability from day shift = 0.0198
probability from swing shift = 8C4/24C4 = 70/106026 = 0.0066
probability from graveyard shift = 6C4/24C4 = 15/106026 = 0.0014
the probability that all 4 selected workers will be from the same shift = 0.0198 + 0.0066 + 0.0014 = 0.0278
(c)
In part (b) we have calculated the probability that selected 4 worker are from same shift. Now in order to determine the probability that at least two different shifts will be represented among the selected workers, we can simply subtract the calculated probability from 1
Hence required probability = 1 - 0.0278 = 0.9722
(d)
Consider the event such that no shift left unrepresented. In this case possible selections are 10C2*8C1*6C1 + 10C1*8C2*6C1 + 10C1*8C1*6C2 = 5040
The selections where at least one of the shifts will be unrepresented are 10626 - 5040 = 5586
hence required probability = 5586/10626 = 0.5257
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