Rose and Liz both belong to a club of 20 members. A committee of 4 is to be selected at
random from the 20 members. Find the probability that both Rose and Liz will be
selected

Answers

Answer 1

Using the hypergeometric distribution, it is found that there is a 0.0316 = 3.16% probability that both Rose and Liz will be  selected.

Hypergeometric distribution:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.

In this problem:

Club has 20 members, hence [tex]N = 20[/tex]The committee has 4 members, hence [tex]n = 4[/tex]Rose and Liz are 2 of the members, hence [tex]k = 2[/tex]

The probability that both are selected is P(X = 2), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,20,4,2) = \frac{C_{2,2}C_{18,2}}{C_{20,4}} = 0.0316[/tex]

0.0316 = 3.16% probability that both Rose and Liz will be  selected.

A similar problem is given at https://brainly.com/question/24826394


Related Questions

Please help. I am not sure how to solve. Please include step by step. Thank you for the help!

Answers

Answer:

[tex]h = \frac{V}{\pi r^{2}}[/tex]

h = 4 cm

Step-by-step explanation:

Given the formula for the volume (V) of a cylinder: V = πr ²h, and the following values for volume and radius:

V = 36π cm³

r = 3 cm

First, solve for h:

V = πr ²h

Divide both sides by πr ²:

[tex]\frac{V}{\pi r^{2} } = \frac{\pi r^{2}h}{\pi r^{2} }[/tex]

[tex]h = \frac{V}{\pi r^{2}}[/tex]

Next, solve for the height of the cylinder by substituting the given values for volume and radius into the formula:

[tex]h = \frac{V}{\pi r^{2}}[/tex]

[tex]h = \frac{36\pi }{\pi (3^{2})}[/tex] → π cancels out.

[tex]h = \frac{36}{9}[/tex]

h = 4 cm

State whether the following angle measures can form a triangle.
A) 90, 90, 35
B) 60, 27, 93
(PLEASE HELP)
(If you could also please help me with question 4 as well I will give you brainliest)

Answers

Answer:

3.b because 60,27,93

Step-by-step explanation:

can you brainliest me

Answer:

3.b

2.155/⅘

Step-by-step explanation:

hope it's helpful

Please help me on this thank you I’ll give brainliest

Answers

Answer:

Eh, you're not getting any help since you lied about "giving brainliest".

Step-by-step explanation:

Which is the smallest integer that makes the inequality 2x + 3 > 5 true?​

Answers

0 is the correct answer;

2*0=0, and 0+3=3.

However if we plug in 1 it does not work you see; 2+1=2, and 2+3 = 5.

It has to be > not =

2

Step-by-step explanation:

because if you subtitute 2 for x you would get

2(2) +3>5

4+3=7

7>5

which makes the inequality true

The average distance from Earth to the Moon is approximately 384,400,000 kilometers.

What is the average distance, in kilometers, from Earth to the Moon written in scientific notation?

A 3.844 x 10^4 kilometers

B 3.844 x 10^5 kilometers

C 3.844 x 10^7 kilometers

D 3.844 x 10^8 kilometers

Answers

9514 1404 393

Answer:

  D.  3.844 × 10^8 kilometers

Step-by-step explanation:

To write the number in scientific notation, put a decimal point after the most significant digits and write the rest of the significant digits after that. Multiply the number by the power of 10 that tells how many digits are between the most significant digit and the decimal point.

Here, the number has 8 digits between the most-significant digit (3) and the decimal point. Any trailing zeros are assumed to be not significant when the number is written without a decimal point. So, the number is written ...

  3.844 × 10^8 km

How much has James earned since the beginning of the year in 2014? (use pay stub) *
1 point
$1,451.28
$3548.72
$5,000

Answers

Can you give more information?

simplify this please

Answers

Answer:

0? I tried solving it myself then I put it into my calculator and both times I got 0

Find the geometric mean between each pair of numbers

Show your work please
Thank you❤️❤️❤️

Answers

Answer:

1.26

Step-by-step explanation:

geometric mean =sqrt((4/5)*2)=sqrt(1.6)=1.26

How to solve 589 divided by 41

Answers

Answer:

14.365

Step-by-step explanation:

do long division or put it in a calculator

help me i nedd help...........

Answers

Answer:

The answer is 10 12/85    Hope you pass!

Convert the units of measure

Answers

Answer:

22.5

Step-by-step explanation:

24 hr in a day

so

540 : 24 = 22.5 or 22 1/2

I NEED ANSWERS TO THESE QUESTIONS


1.How are the areas of a circle and a parallelogram related?


2. Find the area of a circle with a radius of 6.9 m to the nearest tenth. Leave your answer in terms of π.


3. The average crop circle is between 100 and 300 ft in diameter. Find the area of a crop circle that is 300 ft in diameter. Use 3.14 for π.


4. A baker makes a giant cookie for special occasions that is 16 in. in diameter. How many 4-in. diameter cookies would it take to equal the area of one giant cookie?


5. Compare and Contrast What is the difference between the circumference and area of a circle

6. Reasoning A round pizza has an area of 254.34 in.2. Explain how to estimate the length and width of the square box needed to package the pizza

Answers

I only have the answer for 1, but !

1. The area of a parallelogram is  base times height. Since the area of that rectangle is twice the area of the circle, then the area of the circle is half the base times the height. It will be half of 2πr· r. The area of the circle will be πr2

1.35 - 0.829 SHOW YOUR WORK​

Answers

Answer:

0.521

Step-by-step explanation:

It's just like subtracting

Please explain step by step how to solve. Thank you

Answers

By doing cross multiply, you'll get

6(p-1) = 8(p+10)

Expand

6p-6 = 8p+80

Arrange

-80-6 = 8p-6p

-86 = 2p

Divide by 2 to find p

-43 = p

Answer:

p =

Step-by-step explanation:

First, we can start by cross multiplying.

p−1p+10=86

(p−1)*(6)=8*(p+10)

6p−6=8p+80

After some simplification, we get:

−2p=86

Then we find out that p = -43

If we put it in, and then simplify that, we will get 8/6

If this helped you, consider marking this as brainliest :)

At the local dairy farm, Kareem buys a 32-oz container of yogurt for $2.56. Jonah buys a 6-oz container of yogurt for $0.48. Are the cost, y, in dollars and the amount of yogurt, x, proportional? Explain. Write an equation to represent this relationship. how do you fill it out.

Answers

Answer:

Step-by-step explanation:

how do you determine volume?

Answers

Answer:   V = πr 2 h

Step-by-step explanation:

To calculate the volume of a cylinder, you must know its height and the radius of the circular base (the distance from the center of the circle to its edge) at the top and bottom. The formula is V = πr 2 h, where V is the Volume, r is the radius of the circular base, h is the height, and π is the constant pi.

class 6 MATHS! is this correct???​

Answers

Answer:

yes Bro it is correct ar u writing an exam

That is the correct answer

a school has 400 feet of fencing to build a set of 3 athletic fields as shown below. What dimensions should they use to build the largest possible athletic complex. Include appropriate units with your answer.

Answers

The area of a shape is the amount of space it occupies.

The dimensions to build the largest possible athletic complex is 100 by 50 feet

Assume the length of the fence is y.

So, we have:

[tex]\mathbf{Area = xy}[/tex]

[tex]\mathbf{Perimeter = 2y + 4x}[/tex]

Substitute 400 for perimeter

[tex]\mathbf{2y + 4x = 400}[/tex]

Divide through by 2

[tex]\mathbf{y + 2x = 200}[/tex]

Make y the subject

[tex]\mathbf{y = 200 -2x}[/tex]

Substitute [tex]\mathbf{y = 200 -2x}[/tex] in [tex]\mathbf{Area = xy}[/tex]

[tex]\mathbf{Area =x(200 - 2x)}[/tex]

[tex]\mathbf{Area =200x - 2x^2}[/tex]

Differentiate

[tex]\mathbf{A' =200 - 4x}[/tex]

Set to 0

[tex]\mathbf{200 - 4x = 0}[/tex]

Collect like terms

[tex]\mathbf{4x = 200}[/tex]

Divide both sides by 4

[tex]\mathbf{x = 50}[/tex]

Recall that: [tex]\mathbf{y = 200 -2x}[/tex]

So, we have:

[tex]\mathbf{y = 200 - 2 \times 50}[/tex]

[tex]\mathbf{y = 200 - 100}[/tex]

[tex]\mathbf{y = 100}[/tex]

Hence, the dimensions to build the largest possible athletic complex is 100 by 50 feet

Read more about areas and perimeters at:

https://brainly.com/question/11957651

Charles has read 180 pages of a book. This is of the total number of pages in the book. If p represents the number of pages in the book, what is p?

Answers

Answer:

More than 180. It needs more info to have an actual answer.

Answer: I believe it would be 180 considering he has 180 pages in a book and you wanna know how many pages he has it would be 180 hoped this helped love ✨

Step-by-step explanation:

Simplify 10/16 to the lowest terms and find an equivalent fraction that has a denominator of 32.

Answers

Answer:

5/8,  20/32

Step-by-step explanation:

Divide 10/16 by 2 as that is the GCF (greatest common factor) = 5/8

To find an equivalent fraction with a denominator of 32 multiply 10/16 by 2 = 20/32

Answer:

5/8; 20/32

Step-by-step explanation:

10/16 = (5 · 2)/(8 · 2) = 5/8 lowest term

 equivalent fraction  5/8 = ?/32  means 32÷ 8 = 4 × 5 =20

5/8 = 20/32

If using 10/16 = ?/32     means 32 ÷ 16 = 2 × 10 = 20

Again 10/16 = 20/32

HELP ME SOLVEEEE !!!!!

Answers

Answer:

y=2

Step-by-step explanation:

y+7=9(y-1)

y+7=9y-9

y-9y=-9-7

-8y=-16

y=2

>> Answer

_________

[tex] \: [/tex]

[tex] \frac{1}{3} (y + 7) = 3(y - 1)[/tex]

[tex] \frac{y + 7}3 = 3(y - 1) [/tex]

[tex]y + 7 = 9(y - 1)[/tex]

[tex]y + 7 = 9y - 9[/tex]

[tex]y - 9y = - 9 - 7[/tex]

[tex] - 8y = - 16[/tex]

y = 2

If lineman works 9 1/2 hours a day on a certain job at $28.70 per hour, what is the pay for a day?

Answers

9.5 x 28.70 = 272.65

ILL give u 35 points if u answer this. i need help

Answers

The answer is 11xy+4x^2t

Consider the equation below. The value of x in terms of h is . The value of x when h = 4 is .

Answers

The value of x when h = 4 is 4.

The given equation is  :   4(x − 3) = h.  We need to find the value of x in terms of h and the value of x when h = 4.So, we will solve this equation by following the steps given below:

Step 1: Distribute 4 by x and 4 by -3. It gives us:4x - 12 = h

Step 2: Add 12 to both sides of the equation. We get:4x - 12 + 12 = h + 124x = h + 12

Step 3: Divide both sides of the equation by 4. We get:x = (h + 12) / 4

Therefore, the value of x in terms of h is x = (h + 12) / 4.

Now, we need to find the value of x when h = 4. We will put h = 4 in the above equation and get the value of x.x = (4 + 12) / 4 = 16 / 4 = 4.

For more such questions on equation

https://brainly.com/question/29174899

#SPJ8

PLEAS HELP!
The diagram shows a convex
polygon.
What is the value of a?

Answers

Answer:

40°

Step-by-step explanation:

56+84=140

180-140=40°

(5x+4)-3x
Solve it.
No scam

Answers

Answer:

=2x+4

Step-by-step explanation:

Let's simplify step-by-step.

5x+4−3x

=5x+4+−3x

Combine Like Terms:

=5x+4+−3x

=(5x+−3x)+(4)

=2x+4

Answer:

2x+4...

Step-by-step explanation:

Hopefully it helps

help please! if correct i will give brainley

Answers

Answer:

The scale factor is 1.5! I hope this helps!

Answer: 1.5

Each measurement:

12/8 = 1.5

9/6 = 1.5

15/10 = 1.5

QUICK!!

fill in the blanks below in order to justify whether or not the mapping shown represents a function.

Answers

Step-by-step explanation:

I don't know what the specific options are to be selected, but I can tell you what the situation is, and you can then pick the fitting options on your screen :

it is not a function, because 5 in set A (the domain) leads to 2 associated (functional result) values in B (the range).

but in order to be a function, every input value must have exactly one resulting output value. which is violated here.

what does N equal because i dont know

Answers

Answer:

N = Natural numbers


Use complete sentences to describe how you can algebraically determine where the solution region is for a quadratic inequality once the
points of intersection have been found.

Answers

Answer:

hwiwj8eie9eiejnebwnw

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