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

five

first​-shift

workers.

The probability of choosing exactly

five

first​-shift

workers is

nothing.

​(Round to three decimal places as​ needed.)

Answer 1

Given a warehouse employs,

28 workers on first shift,

15 workers on second shift,

10 workers on third shift.

Now eight workers are chosen at random and they are to be interviewed about the work environment.

We need to find the probability of choosing exactly five first shift workers.

Now total number of workers are 53.

Now the number of ways we can choose 8 workers from 53 workers is= 53C8

The number of ways we can choose 5 first shift workers from 28 workers is=28C5

So out of the 8 workers chosen randomly we had already chosen 5 first shift workers so the remaining 3 workers should be chosen from the second or the third shift workers and that can be done in=(15+10)C3=25C3 ways

Therefore the probability of choosing exactly five first shift workers is=(28C5 * 25C3)/53C8

Therefore the probability of choosing exactly five first shift workers is 0.255