Mathematics, 20.06.2020 16:57 uhhgray

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 4 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 4 workers has the same chance of being selected as does any other group (drawing 4 slips without replacement from among 24). (a) How many selections result in all 4 workers coming from the day shift? What is the probability that all 4 selected workers will be from the day shift? (Round your answer to four decimal places.)
(b) What is the probability that all 4 selected workers will be from the same shift? (Round your answer to four decimal places.)
(c) What is the probability that at least two different shifts will be represented among the selected workers? (Round your answer to four decimal places.)
(d) What is the probability that at least one of the shifts will be unrepresented in the sample of workers? (Round your answer to four decimal places.)

Answers: 3

Show answers

Answers

Answer from: rachel2005smith

The probability that all 4 selected workers will be from the day shift is, = 0.0198

The probability that all 4 selected workers will be from the same shift is = 0.0278

The probability that at least two different shifts will be represented among the selected workers is = 0.9722

The probability that at least one of the shifts will be unrepresented in the sample of workers is P(A∪B∪C) = 0.5257

To solve this question properly, we will need to make use of the concept of combination along with set theory.

What is Combination?

In mathematical concept, Combination is the grouping of subsets from a set without taking the order of selection into consideration.

The formula for calculating combination can be expressed as:

$\mathbf{(^n _r) =\dfrac{n!}{r!(n-r)! }}$

From the parameters given:

Workers employed on the day shift = 10Workers on swing shift = 8Workers on graveyard shift = 6

A quality control consultant is to select 4 of these workers for in-depth interviews:

Using the expression for calculating combination:

(a)

The number of selections results in all 4 workers coming from the day shift is :

$\mathbf{(^n _r) = (^{10} _4)}$

$\mathbf{=\dfrac{(10!)}{4!(10-4)!}}$

= 210

The probability that all 5 selected workers will be from the day shift is,

$\begin{array}{c}\\P\left( {{\rm{all \ 4 \ selected \ workers\ will \ be \ from \ the \ day \ shift}}} \right) = \dfrac{{\left( \begin{array}{l}\\10\\\\4\\\end{array} \right)}}{{\left( \begin{array}{l}\\24\\\\4\\\end{array} \right)}}\\\end{array}$

$\mathbf{= \dfrac{210}{10626}} \\ \\ \\ \mathbf{= 0.0198}$

(b) The probability that all 4 selected workers will be from the same shift is calculated as follows:

P( all 4 selected workers will be) $\mathbf{= \dfrac{ \Big(^{10}_4\Big) }{\Big(^{24}_4\Big)}+\dfrac{ \Big(^{8}_4\Big) }{\Big(^{24}_4\Big)} + \dfrac{ \Big(^{6}_4\Big) }{\Big(^{24}_4\Big)}}$

where;

$\mathbf{\Big(^{8}_4\Big) = \dfrac{8!}{4!(8-4)!} = 70}$

$\mathbf{\Big(^{6}_4\Big) = \dfrac{6!}{4!(6-4)!} = 15}$

P( all 4 selected workers is:)

$\mathbf{=\dfrac{210+70+15}{10626}}$

The probability that all 4 selected workers will be from the same shift is = 0.0278

(c)

The probability that at least two different shifts will be represented among the selected workers can be computed as:

$= 1-\dfrac{ (^{10}_4) }{(^{24}_4)}+\dfrac{ (^{8}_4) }{(^{24}_4)} + \dfrac{ (^{6}_4) }{(^{24}_4)}$

$=1 - \dfrac{210+70+15}{10626}$

= 1 - 0.0278

= 0.9722

The probability that at least two different shifts will be represented among the selected workers is = 0.9722

(d)

The probability that at least one of the shifts will be unrepresented in the sample of workers is:

$P(AUBUC) = \dfrac{(^{6+8}_4)}{(^{24}_4)}+ \dfrac{(^{10+6}_4)}{(^{24}_4)}+ \dfrac{(^{10+8}_4)}{(^{24}_4)}- \dfrac{(^{6}_4)}{(^{24}_4)}-\dfrac{(^{8}_4)}{(^{24}_4)}-\dfrac{(^{10}_4)}{(^{24}_4)}+0$

$P(AUBUC) = \dfrac{(^{14}_4)}{(^{24}_4)}+ \dfrac{(^{16}_4)}{(^{24}_4)}+ \dfrac{(^{18}_4)}{(^{24}_4)}- \dfrac{(^{6}_4)}{(^{24}_4)}-\dfrac{(^{8}_4)}{(^{24}_4)}-\dfrac{(^{10}_4)}{(^{24}_4)}+0$

$P(AUBUC) = \dfrac{1001}{10626}+ \dfrac{1820}{10626}+ \dfrac{3060}{10626}-\dfrac{15}{10626}-\dfrac{70}{10626}-\dfrac{210}{10626} +0$

The probability that at least one of the shifts will be unrepresented in the sample of workers is P(A∪B∪C) = 0.5257

Learn more about combination and probability here:

Answer from: Quest

the answer is. -82562234434584

step-by-step explanation:

Answer from: Quest

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

Another question on Mathematics

Mathematics, 21.06.2019 15:10

Marcus needs to rewrite f(x) = x2 + 6x + 4 in vertex form.

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

Suppose you just purchased a digital music player and have put 8 tracks on it. after listening to them you decide that you like 4 of the songs. with the random feature on your player, each of the 8 songs is played once in random order. find the probability that among the first two songs played (a) you like both of them. would this be unusual? (b) you like neither of them. (c) you like exactly one of them. (d) redo () if a song can be replayed before all 8 songs are played.

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

You’re giving a cube with a length of 2.5 cm and a width of 2.5 cm and a high of 2.5 cm you place it on a scale and it is 295 g calculate the density

Answers: 1

Answer

Mathematics, 22.06.2019 04:30

Ribbon a is 1/3 meters long. it is 2/5 meters shorter than ribbon b. what's the total length of 2 ribbons?

Answers: 1

Answer

You know the right answer?

A production facility employs 10 workers on the day shift, 8 workers on the swing shift, and 6 worke...