A production facility employ 11 workers on the day shift, 9 workers on swing shi
ID: 3158732 • Letter: A
Question
A production facility employ 11 workers on the day shift, 9 workers on swing shift and 5 workers on the graveyard shift. A quality control consultant is to make a random selection of 5 of those workers (without replacement) for in-depth interviews.
What is the probability that all 5 workers will be from the same shift?
What is the probability that at least two different shifts will be represented among selected workers?
What is the probability that exactly one of the shifts will not be represented in the sample of selected workers?
Explanation / Answer
1. the probability that all 5 workers will be from the same shift= [11C5 + 9C5 + 5C5] / 25C5=589/53130=0.0111
2. the probability that at least two different shifts will be represented among selected workers
= the complement of the probability that all 5 workers will be from the same shift=1-0.0111=0.9889
3. the probability that exactly one of the shifts will not be represented in the sample of selected workers
= Probability that workers are selected from day shift and swing shift or swing shift and graveyard shift or day shift and graveyard shift
=[20C5+14C5+16C5]/25C5=21874/53130=0.4117
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