A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10 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 45). (Enter your answers to four decimal places.) Required:
a. How many selections result in all 7 workers coming from the day shift?
b. What is the probability that all 7 selected workers will be from the day shift?
c. What is the probability that all 7 selected workers will be from the same shift?
d. What is the probability that at least two different shifts will be represented among the selected workers?
e. What is the probability that at least one of the shifts will be unrepresented in that sample of workers?

Step-by-step explanation:

Total number of workers = 20+ 15 + 10 = 45

Suppose 6 workers are selected from 45 workers, the number of ways they can be selected is ways

If 7 workers are selected from 20 workers on a day shift;

Then, the number of ways to select 7 members from a group of 20 is ways;

∴

P( all 7 selected workers will be from the day shift) is:

= 0.0095

The possible number of ways to select all day shift workers is:

The  possible number of ways to select all swing shift workers is:

The possible number of ways to select all graveyard shift workers is:

∴

The probability that all selected workers are from the same shift is:

= 0.0095 + 0.00079 + 0.000015

= 0.010305

P(selected workers are from at least two different shifts)

= 1 - P(selected workers are from 1 shift from any of the 3 shifts)

= 1 - 0.010305

= 0.989695

≅ 0.9897

We can determine the probability that at least one shift is unrepresented through the following ways:

Let assume that:

event that day shift is unrepresented

event that swing shift is unrepresented

event that graveyard shift is unrepresented

Thus; = event that all of them are drawn from graveyard shift.

event that all are drawn from swing shift

event that they are all drawn from day shift.

So;

Probability (that at least one shift is unrepresented) is:

= 0.0590 + 0.2499 + 0.8256 - 0.000015 - 0.00079 - 0.0095 + 0

≅ 1.124

25/14 or 1.

step-by-step explanation:

the dots mean that it has infinitely more numbers behind it