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 5 of these workers for in- depth interviews. Suppose the selection is made in such a way that any particular group of 5 workers has the same chance of being selected as does any other group (drawing 5 slips without replacement from among 24). a) How many selections result in all 5 workers coming from the day shift? 252 selections What is the probability that all 5 selected workers will be from the day shift? (Round your answer to four decimal places.) b) What is the probability that all S 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.) Submit Answer Save Progress Practice Another Version 4. ,,-3 points DevoreStat9 2.?.504.xP. a My Notes

Explanation / Answer

a)
Total workers = 24
Day shift workers = 10

we need to select 5 workers from day shift workers

Required probability = 10C5 / 24C5
= 0.0059

b)

we need to select 5 from day shift , 5 from swing shift and 5 from graveyard shift

Required probability = (10C5/24C5) + (8C5/24C5) + (6C5/24C5)
= 0.0074

c)
The opposite event of the event that at least two different shifts will be represented among the selected workers is the event in B.

Required probability = 1 - [(10C5/24C5) + (8C5/24C5) + (6C5/24C5)]
= 0.9926

d)
Suppose that the event that only day shifts be unrepresented is A1, only swing shifts be unrepresented is A2, only graveyard shifts be unrepresented is A2.
The probability that at least one of the shifts will be unrepresented in the sample of workers is

P(A1 union A2 union A3) = P(A1) + P(A2) + P(A3) - ?P(A1?A2)?P(A1?A3)?P(A3?A2)+P(A1?A2?A3)

= (14C5/24C5) + (16C5/24C5) + (18C5/24C5) - (6C5/24C5) - (8C5/24C5) -(10C5/24C5) + 0
= 0.3441

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