Question

A warehouse employs 28 workers on first shift, 15 workers on second shift, and 10 workers on third shift. Eight workers are chosen at random to be interviewed about the work environment. Find the probability of choosing exactly two second shift workers and two third shift workers. The probability of choosing two second shift workers and two third shift workers is (Round to three decimal places as needed.) .

Answer 1

Population:

First Shift = 28

Second shift = 15

Third shift = 10

Total workers = 53

Sample:

First Shift = 4

Second shift = 2

Third shift = 2

Total workers = 8

8 Workers can selected from 53 Workers in

53! 5308 = (53) = 5 8/ 8!(53 _ 8) = 886322710

4 First shift Workers can selected from 28 First Shift Workers in

2804 = (-1) = 2123) = 20475

2 Second shift Workers can selected from 15 Second Shift Workers in

1502 = (15) = _15!_ 2 + 2!(15 – 2)!

2 Third shift Workers can selected from 10 Third Shift Workers in

10C2 = 10 10! 2 ) + 2!(10 – 2)!

So,

Required Probability = 20475 X 105 X 45 / 886322710

                             = 0.109

So,

Answer is:

0.109