Mathematics, 13.07.2020 23:01 Meirna

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 7 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 7 workers has the same chance of being selected as does any other group (drawing 7 slips without replacement from among 45). 1. How many selections result in all 7 workers coming from the day shift?
2. What is the probability that all 7 selected workers will be from the day shift?
3. What is the probability that all 7 selected workers will be from the same shift?
4. What is the probability that at least two different shifts will be represented among the selected workers?
5. What is the probability that at least one of the shifts will be un-represented in that sample of workers?

Answers: 2

Show answers

Answers

Answer from: Alijahvalles7443

1. 77520

2. P_1 = 0.0017

3. P_2 = 0.0019

4. P_3 = 0.9981

5. P_4 = 0.2036

Step-by-step explanation:

The number of ways or combinations in which we can select x elements from a group of n can be calculated as:

$nCx = \frac{n!}{x!(n-x)!}$

So, there are 77520 selections that result in all 7 workers coming from the day shift. It is calculated as:

$20C7 = \frac{20!}{7!(20-7)!}=77520$

At the same way, the total number of selections of 7 workers from the 45 is 45C7, so the probability that all 7 selected workers will be from the day shift is:

$P_1=\frac{20C7}{45C7} =0.0017$

The probability that all 7 selected workers will be from the same shift is calculated as:

$P_2=\frac{20C7+15C7+10C7}{45C7} =0.0019$

Because the consultant can select all workers from the day shift (20C7) or can select all workers from the swing shift (15C7) or can select all workers from the graveyard shift (10C7).

On the other hand, the probability that at least two different shifts will be represented among the selected workers is the complement of the probability that all 7 selected workers will be from the same shift. So it is calculated as:

P_3 = 1- P_2=1 - 0.0019 = 0.9981

Finally, the probability that at least one of the shifts will be un-represented in that sample of workers is:

$P_4=\frac{25C7+30C7+35C7}{45C7} =0.2036$

Where 25C7 is the number of ways to select all 7 workers from swing or graveyard shift, 30C7 is the number of ways to select all 7 workers from day or graveyard shift and 35C7 is the number of ways to selects all 7 workers from day shift and swing shift.

Answer from: Quest

33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333212222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111411111110

step-by-step explanation:

Choose the function that the graph represents

Answer from: Quest

40% off the regular price is the correct answer.

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 18:00

Asquare has a perimeter of sixteen centimeters. what is the length of each of its sides? a. 8 cm c. 9 cm b. 4 cm d. 10 cm select the best answer from the choices

Answers: 2

Answer

Mathematics, 21.06.2019 19:30

The figure below shows rectangle abcd and the triangle eca on a coordinate plane.which of the following expressions represents the perimeter of triangle of triangle eca in units

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

If a 36 inch yardstick casts a 21 foot shadow, how tall is a building whose shadow is 168 feet? what is the scale factor

Answers: 1

Answer

Mathematics, 21.06.2019 22:30

We have 339 ounces of jam to be divided up equally for 12 people how muny ounces will each person get

Answers: 1

Answer

You know the right answer?

A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10 wor...