Three times each day, a quality engineer samples a component from a recently manufactured batch and tests it. Each part is classified as conforming (suitable for its intended use), downgraded (unsuitable for the intended purpose but usable for another purpose), or scrap (not usable). An experiment consists of recording the categories of the three parts tested in a particular day.
a. Let A be the event that all the parts fall into the same category. List the outcomes in A.
b. Let B be the event that there is one part in each category. List the outcomes in B.
c. Let C be the event that at least two parts are conforming. List the outcomes in C.
d. List the outcomes in A⋂C
e. List the 27 outcomes in the sample space.
f. List the outcomes in A U B.
g. List the outcomes in A⋂Cc
h. List the outcomes in Ac⋂C.
i. Are events A and C mutually exclusive? Explain.
j. Are events B and C mutually exclusive? Explain.

Answers

Answer 1

Answer:

a. Outcomes of A = { (C,C,C) , (D,D,D), (S,S,S) }

b. Outcomes of B = { (C,D,S),(C,S,D),(D,C,S),(D,S,C),(S,C,D),(S,D,C) }

c. Outcomes of C = { (C,C,C),(C,C,D),(C,C,S),(C,D,C),(C,S,C),(D,C,C),(S,C,C) }

d. Outcomes of A⋂C = { (C,C,C) }

e. Outcomes of Sample space = { (C,C,C), (C,C,D), (C,C,S), (C,D,C), (C,D,D), (C,D,S), (C,S,C), (C,S,D), (C,S,S), (D,C,C), (D,C,D),(D,C,S), (D,D,C), (D,D,D), (D,D,S), (D,S,C), (D,S,D), (D,S,S),   (S,C,C), (S,C,D), (S,C,S), (S,D,C), (S,D,D), (S,D,S), (S,S,C), (S,S,D), (S,S,S) }

f. Outcomes of A U B = { (C,C,C) , (D,D,D), (S,S,S), (C,D,S),(C,S,D),(D,C,S),(D,S,C),(S,C,D),(S,D,C) }

g. Outcomes of A⋂[tex]C^{c}[/tex] = { (D,D,D), (S,S,S) }

h. Outcomes of [tex]A^{c}[/tex]⋂C = {(C,C,D),(C,C,S),(C,D,C),(C,S,C),(D,C,C),(S,C,C)}

i. Events A and C are not mutually exclusive

j. Events B and C are mutually exclusive

Step-by-step explanation:

Given - Three times each day, a quality engineer samples a component

             from a recently manufactured batch and tests it. Each part is

             classified as conforming (suitable for its intended use),  

             downgraded (unsuitable for the intended purpose but usable for  

             another purpose), or scrap (not usable). An experiment consists

             of recording the categories of the three parts tested in a particular

              day.

To find - a. Let A be the event that all the parts fall into the same

                  category. List the outcomes in A.

              b. Let B be the event that there is one part in each category.

                  List the outcomes in B.

              c. Let C be the event that at least two parts are conforming.

                  List the outcomes in C.

              d. List the outcomes in A⋂C

              e. List the 27 outcomes in the sample space.

               f. List the outcomes in A U B.

              g. List the outcomes in A⋂[tex]C^{c}[/tex]

              h. List the outcomes in ⋂C.

              i. Are events A and C mutually exclusive? Explain.

              j. Are events B and C mutually exclusive? Explain.

Proof -

Let

Conforming part = C

Downgraded part = D

Scrap part = S

a.)

Given , Let A be the event that all the parts fall into the same category.

Outcomes of A = { (C,C,C) , (D,D,D), (S,S,S) }

b.)

Given, Let B be the event that there is one part in each category.

Outcomes of B = { (C,D,S),(C,S,D),(D,C,S),(D,S,C),(S,C,D),(S,D,C) }

c.)

Given,  Let C be the event that at least two parts are conforming.

Outcomes of C = { (C,C,C),(C,C,D),(C,C,S),(C,D,C),(C,S,C),(D,C,C),(S,C,C) }

d.)

Outcomes of A⋂C = { (C,C,C) }

e.)

Outcomes of Sample space = { (C,C,C), (C,C,D), (C,C,S), (C,D,C), (C,D,D), (C,D,S), (C,S,C), (C,S,D), (C,S,S), (D,C,C), (D,C,D),(D,C,S), (D,D,C), (D,D,D), (D,D,S), (D,S,C), (D,S,D), (D,S,S),   (S,C,C), (S,C,D), (S,C,S), (S,D,C), (S,D,D), (S,D,S), (S,S,C), (S,S,D), (S,S,S) }

f.)

Outcomes of A U B = { (C,C,C) , (D,D,D), (S,S,S), (C,D,S),(C,S,D),(D,C,S),(D,S,C),(S,C,D),(S,D,C) }

g.)

Outcomes of [tex]C^{c}[/tex]  =  {  (C,D,D), (C,D,S), (C,S,D), (C,S,S), (D,C,D),(D,C,S), (D,D,C), (D,D,D), (D,D,S), (D,S,C), (D,S,D), (D,S,S), (S,C,D), (S,C,S), (S,D,C), (S,D,D), (S,D,S), (S,S,C), (S,S,D), (S,S,S) }

Outcomes of A⋂[tex]C^{c}[/tex] = { (D,D,D), (S,S,S) }

h.)

Outcomes of [tex]A^{c}[/tex] = {(C,C,D), (C,C,S), (C,D,C), (C,D,D), (C,D,S), (C,S,C), (C,S,D), (C,S,S), (D,C,C), (D,C,D),(D,C,S), (D,D,C),  (D,D,S), (D,S,C), (D,S,D), (D,S,S),   (S,C,C), (S,C,D), (S,C,S), (S,D,C), (S,D,D), (S,D,S), (S,S,C), (S,S,D), }

Outcomes of [tex]A^{c}[/tex]⋂C = {(C,C,D),(C,C,S),(C,D,C),(C,S,C),(D,C,C),(S,C,C) }

i.)

As we two that Two events A and C are mutually exclusive iff A ∩ C = ∅

Now,

A ∩ C = { (C,C,C) }

⇒Events A and C are not mutually exclusive.

j.)

As we two that Two events B and C are mutually exclusive iff B ∩ C = ∅

Now,

B ∩ C = ∅

⇒Events B and C are mutually exclusive.


Related Questions

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Answers

Answer:

[tex](p - q)(x) = (x -1) (x - 4)[/tex]

Step-by-step explanation:

Given

[tex]p(x) = x^2 - 1[/tex]

[tex]q(x) = 5(x - 1)[/tex]

Required

(p - q)(x)

This is represented as:

[tex](p - q)(x) = p(x) - q(x)[/tex]

[tex](p - q)(x) = x^2 - 1 - 5(x - 1)[/tex]

[tex](p - q)(x) = x^2 - 1 - 5x + 5[/tex]

Collec like terms

[tex](p - q)(x) = x^2 - 5x + 5 - 1[/tex]

[tex](p - q)(x) = x^2 - 5x + 4[/tex]

Expand

[tex](p - q)(x) = x^2 -4x - x + 4[/tex]

Factorize

[tex](p - q)(x) = x(x -4) - 1(x - 4)[/tex]

[tex](p - q)(x) = (x -1) (x - 4)[/tex]

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Step-by-step explanation:

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Answers

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Answers

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Parentheses
Exponents
Multiplication
Division
Add
Subtract
When it comes down to multiplication and division you do whichever comes first , left to right same with add and subtract so..
Step1: 2 squared = 4
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Step3: 1x10=10
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Identify the parent function that can be used to graph the function f(x)=2[x-6]

Answers

Answer:

F(x) =2(1/2 x2-6x) +C

Step-by-step explanation:

Hope it helps

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Step-by-step explanation:

1. The parent function of a Function part full is shown below:

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f(x-6)=[x-6] (The function is shifted 6 units on the positive x-axis)

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Sharon is using a calculator to find out how many hours she has spent on a certain job.She divides,and her display reads:​

Answers

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Answers

Answer:

48π

Step-by-step explanation:

Given that,

The radius of the sphere is increasing at a rate of 3cm/minute, [tex]\dfrac{dr}{dt}=3\ cm/minute[/tex]

The volume of a sphere is given by :

[tex]V=\dfrac{4}{3}\pi r^3[/tex]

Differentiating both sides wrt t.

[tex]\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3r^2\times \dfrac{dr}{dt}\\\\=4\pi r^2\times \dfrac{dr}{dt}[/tex]

Put r = 2 cm and dr/dt = 3 cm/minute

So,

[tex]\dfrac{dV}{dt}=4\pi r^2\times \dfrac{dr}{dt}\\\\\dfrac{dV}{dt}=4\pi \times 2^2\times 3\\\\\dfrac{dV}{dt}=48\pi[/tex]

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Answers

9514 1404 393

Answer:

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Step-by-step explanation:

Let 'a' and 'p' stand for the prices of apple and pumpkin pies, respectively. Then the two sales are described by ...

  4a +5p = 86

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Subtract half the second equation from the first to eliminate the 'a' variable.

  (4a +5p) -(1/2)(8a +2p) = (86) -(1/2)(92)

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  p = 10 . . . . . . . divide by 4

Substitute into the first equation:

  4a + 5(10) = 86

  4a = 36 . . . . . subtract 50

  a = 9 . . . . . . . divide by 4

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Answers

Answer:

32.1869

Step-by-step explanation:

You can use an online converter!

You can look up Miles to KM

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Answers

g(x) = (1.6)x − 9 + 5

Answer:

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Two boards are placed end to end to make a walkway. One board is 5 feet 11 inches long, and the other board is 4 feet 6 inches long. How long is the walkway?
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Answers

Answer:

10 feet 5 inches long

Step-by-step explanation:

12 inches = 1 foot

11 inches + 6 inches = 17 inches = 1 foot 5 inches

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Therefore, the walking board is 10 feet 5 inches long



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Answers

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Step-by-step explanation:

Take the equation

2(4y)+4(3r)

Distribute the 2 and 4 into the parenthesis'

8y+12r

Let's simply:
___________
2(4y) + 4(3r)
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Answers

Answer:

Quantity of  cranberry juice = 95  ml  

Quantity of  orange   juice = 95  ml

Step-by-step explanation:

Step 1

Given ,

We have  80% cranberry juice and  4% of  orange juice.

We have to find how much each should be mixed to make 190 ml of a  60% cranberry-orange juice blend.

Step 2

Let's assume

Quantity of  cranberry juice =x ml  

Quantity of  orange   juice =y  ml  

Then,

x + y = 190

and

x×80100 +y×4100 = 190×60100  

⇒ 0.8x+0.4y = 114    

⇒ 2x+y = 285  

⇒ y = 285−2x  

Step 3

Substituting   y = 285−2x  in  x + y = 190  

⇒ x+285−2x = 190  

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⇒ −x = −95  

⇒ x = 95  ml  

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⇒ 95 + y = 190  

⇒ y = 190−95  

⇒ y = 95 ml  

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Quantity of  cranberry juice =95  ml  

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Answers

Answer:

He can be 99% confident that the mean number of calls per day is between 266.5 and 292.3.

Step-by-step explanation:

Confidence interval:

A confidence interval is symmetric, which means that the difference between the sample mean and the lower bound is the same as the difference between the upper bound and the sample mean.

In this question:

Sample mean: 279.4 calls

Lower bound: 266.5 calls

Upper bound: x calls

Due to the symmetry of the confidence interval:

[tex]x - 279.4 = 279.4 - 266.5[/tex]

[tex]x = 12.9 + 279.4[/tex]

[tex]x = 292.3[/tex]

So

He can be 99% confident that the mean number of calls per day is between 266.5 and 292.3.

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Answers

Answer:

Step-by-step explanation:

B

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Answer:

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Answers

Answer:

she would probably drive 520 miles in she is driving 65 mph for a whole 8 hours

Step-by-step explanation:

Answer:

520

Step-by-step explanation:

This is a very simple explanation.

Mrs. Garcia drives eight hours...at 65mphs throughout the trip.

How many miles has she drove?

All you need to do is multiply 8x65 and you will get 520.

Mrs. Garcia drove a total of 520 miles.

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Answers

Answer:8.99 cm

Step-by-step explanation:

Answer:

[tex]8.995[/tex]cm

Step-by-step explanation:

The circumference formula is: [tex]C=2\pi r[/tex]

We are given the circumference, which is 56.52cm.

The question wants us to find the radius, r.

To achieve this, we must solve for r.

Plugging in 56.52 for C we get:

[tex]56.52=2\pi r[/tex]

Dividing both sides by [tex]2\pi[/tex], we find r:[tex]8.995[/tex]

[tex]\frac{56.52}{2\pi } =r[/tex]

[tex]8.995[/tex]≈[tex]r[/tex]

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Answers

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Answers

Answer:

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Step-by-step explanation:

Answer:

4x

Step-by-step explanation:

x in this case would be the number

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Answers

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5/4

Answers

Answer:

1 1/4

Step-by-step explanation:

4/4 + 1/4 = 5/4

4/4 = 1

so 1 1/4

Answer: 1  1/4

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Answer AND Step-by-step explanation:

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Complementary Angles Theorem - two angles that are next to each other and add up to 90 degrees.

Vertical Angles Theorem - Angles that are directly across from each other made by an intersection will have the same angle value.

#teamtrees #PAW (Plant And Water)

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Answers

9514 1404 393

Answer:

  (b)  120°

Step-by-step explanation:

The points on the figure are 120° apart, so each will replace the previous when the figure is rotated 120°.

The figure has 120° rotational symmetry.

__

That is also called "order 3 rotational symmetry" as there are three positions a point can be in that will make the figure look identical.

Answer:

B. 120 & D. 240 since they are both multiples of 120

Step-by-step explanation:

Hi! The person who explained it before me helped but didn't give the exact answer so I just wanted to say what it was so nobody got confused.

Have a nice day and hope this helps! :)

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Answers

Answer:

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Step-by-step explanation:

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Answer:

just shade in the same thing

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Answers

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Step-by-step explanation:

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WILL GIVE BRAINIEST

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Answers

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I don't know the answer but have a site that helps me with math, its called

Step-by-step explanation:

Just check it out

PLEASE HELP DUE TONIGHT

Answers

Answer:

The answer should be 20,000 feet

Step-by-step explanation:

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c= 10000/sin 30

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