Question

A production facility employs 10 workers on the day shift, 8 workers on the swing shift, and 6 workers on the graveyard shift. A quality control consultant is to select 6 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 6 workers has the same chance of being selected as does any other group (drawing 6 slips without replacement from among 24).
Required:
a. How many selections result in all 5 workers coming from the day shift?
b. What is the probability that all 5 selected workers will be from the day shift? (Round your answer to four decimal places.)
c. What is the probability that all 5 selected workers will be from the same shift? (Round your answer to four decimal places.)
d. What is the probability that at least two different shifts will be represented among the selected workers? (Round your answer to four decimal places.)
c. What is the probability that at least one of the shifts will be unrepresented in the sample of workers?

Answer 1

Answer:

252 ; 0.0059 ; 0.0074 ; 0.9926

Step-by-step explanation:

Day shift = 10

Swing shift = 8

Graveyard shift = 6

Total number of workers = 24

A.) Number of selections resulting in 5 workers coming from day shift :

10C5 = 10! ÷ (10-5)!5!

= (10*9*8*7*6) / (5*4*3*2*1)

= 252

B.) All 5 workers coming from day shift :

Required outcome = 10C5

Total possible outcomes = 24C5

10C5 ÷ 24C5

252 ÷ 42504

= 0.0059288

= 0.0059

C.) 5 selected workers are from the same shift :

[day shift + swing shift + graveyard shift] / total possible outcomes

[(10C5) + (8C5) + (6C5)] ÷ 24C5

(252 + 56 + 6) / 42504

= 0.0074

D.) What is the probability that at least two different shifts will be represented among the selected workers?

1 - [[(10C5) + (8C5) + (6C5)] ÷ 24C5]

1 - 0.0073875

= 0.9926124

= 0.9926