Question

A production facility employs 16 workers on the day shift, 14 workers on the swing shift, and 8 workers on the graveyard shift. A quality control consultant is to randomly select 6 of these workers for in-depth interviews. (a) What is the probability that all 6 selected workers will be from the same shift? (b) What is the probability that at least two different shifts will be represented among the selected workers? (c) What is the probability that exactly 2 of the workers in the sample come from the day shift?

Answer 1

Solution:

   We are given that: A production facility employs

16 workers on the day shift,

14 workers on the swing shift, and

8 workers on the graveyard shift.

Thus total number of workers = 16+14+8=38

A quality control consultant is to randomly select 6 of these workers for in-depth interviews.

Part a) Find the probability that all 6 selected workers will be from the same shift.

That is:

P(all 6 selected workers will be from the same shift) = P( All 6 workers from Day shift or All 6 workers from Swing shift or All 6 workers from graveyard shift)

P(all 6 selected workers will be from the same shift) = P( All 6 workers from Day shift)

                              + P(All 6 workers from Swing shift) + P(All 6 workers from graveyard shift)

P(all 6 selected workers will be from the same shift)

where

and

Thus

P(all 6 selected workers will be from the same shift)

( Kindly please check number of decimal places that we have to round. it is not mentioned in the given question)

Part b) Find the probability that at least two different shifts will be represented among the selected workers.

P( At least two different shift) = .....?

P( At least two different shift) = 1 - P( All represented exactly 1 shift ( same shift) )

P( At least two different shift) = 1 - 0.003999

P( At least two different shift) =0.996001

P( At least two different shift) = 0.9960

Part c) Find the probability that exactly 2 of the workers in the sample come from the day shift.

P( 2 workers from Day shift ) = ....?

P( 2 workers from Day shift ) = P( 2 from day shift and remaining 4 from (14+8)=22 others )

P( 2 workers from Day shift )

where

thus

P( 2 workers from Day shift )

( Kindly please check number of decimal places that we have to round. it is not mentioned in given question)