A production facility employs 18 workers on the day shift, 14 workers on the swi

Question

A production facility employs 18 workers on the day shift, 14 workers on the swing shift, and 9 workers on the graveyard shift. A quality control consultant is to randomly select 5 of these workers for in-depth interviews. What is the probability that all 5 selected workers will be from the same shift? What is the probability that at least two different shifts will be represented among the selected workers? What is the probability that exactly 3 of the workers in the sample come from the day shift?

Explanation / Answer

Answer:

a).

total workers= 18+14+9=41

Number of ways selecting 5 from 41 workers= 41C5

Number of ways selecting 5 from the same shift = 18C5 +14C5 +9C5

The required Probability = (18C5 +14C5 +9C5) / 41C5

=(8568+2002+126) /749398

=0.014273

b).

P( atleast two different shifts represented)

= 1-P( all from same shift)

=1-0.014273

=0.985727

c).

P( exactly 3 from day shift)

=(18C3*23C2) / 41C5

=816*253 / 749398

=0.275485

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