The probability of an event under the uniform distribution - random permutations. A class with n kids lines up for recess. The order in which the kids line up is random with each ordering being equally likely. There are two kids in the class named Celia and Felicity. Give an expression for each of the probabilities below as a function of n. Simplify your final expression as much as possible so that your answer does not include any expressions of the form (ab)(ab).
(a) What is the probability that Celia is first in line?
(b) What is the probability that Celia is first in line and Felicity is last in line?
(c) What is the probability that Celia and Felicity are next to each other in the line?

Answers

Answer 1

Answer:

a)

the probability that Celia is first in line is 1/n.

b)

the probability that Celia is first in line and Felicity is last in line is 1/n(n-1)

c)

the probability that Celia and Felicity are next to each other in the line is 2/n

 

Step-by-step explanation:

Given the data in question;

a) Celia is first in line?

the total ways are; n! to place n kids in n places in orderly fashion.

now, if Celia is the first kid, we have to order remaining n-1 kids

(n-1)! / n! = 1/n

therefore, the required probability is 1/n.  

b)  Celia is first in line and Felicity is last in line?

the total ways are; n! to place n kids in n places in orderly fashion,

now, if Celia is the first and Felicity is the last kid, we order the remaining n - 2 kids, which can be done in (n-2)!

(n-2)! / n! = 1 / n(n-1)

therefore, the required probability is 1 / n(n-1)

c) Celia and Felicity are next to each other in the line

the total ways are; n! to place n kids in n places in orderly fashion,

now, if Celia and Felicity as single object, so that they can be put together, we arrange n-1 objects which can be done in (n-1)! ways.

But also these 2 can change the place so in total there are 2(n-1)! ways.

2(n-1)! / n! = 2/n

Therefore, the required probability is 2/n


Related Questions

Hey guys I need help asap

A salesman earns 15% commission on each household appliance he sells. If he sells 6 toasters at $32 each, what is the commission that he earned?

Answers

Answer:

$28.8

Step-by-step explanation:

6x32=192

15% of 192 is 28.8

Please help!! PLEASE!!!

Answers

Answer:

30%

Step-by-step explanation:

subtract the post-discount price from the pre-discount price

64.99 - 45.49 = 19.50

divide the answer by the original price

[tex]\frac{19.50}{64.99}[/tex] = 0.30

multiply the answer by 100

0.30 x 100 = 30%

to check:

take the original number and multiply it by the decimal form of the percentgae:

64.99 x 30% (0.30) = 19.50

take the answer and subtract it from the orginal answer

64.99 - 19.50 = 45.49

Solve for x (use steps i need to learn this pls)

Answers

Answer:

x = 14

Step-by-step explanation:

The figure shows two chords intersecting each other. Based on the Theorem of Intersecting chords, the product the segments of each chord is equal to the product of the other. This means:

24*x = 21*16

24x = 336

Divide both sides by 24

24x/24 = 336/24

x = 14

A piece of wood is 3 1/2 feet long how many total inches long is it?

Answers

Answer:

42 inches

Step-by-step explanation:

1 foot is 12 inches

12 times 3=36

12 divided by 2=6

36+6=42

WILL MARK BRAINLEST AND WILL GET 5 STARS REVIEW
Tom’s Taxis charges a fixed rate of $4 per ride plus $0.50 per mile. Carla’s Cabs does not charge a fixed rate but charges $1.00 per mile.
a. Write an equation that represents the cost of Tom’s Taxis.
b. Write an equation that represents the cost of Carla’s cabs.

Answers

Answer:

a. y= 4 + 0.50x  b. y= 1.00x

Step-by-step explanation:

Answer:

a. y = 0.5x +4  b. y = x

Step-by-step explanation:

a. Tom’s Taxis charges a fixed rate of $4 per ride plus $0.50 per mile.

m  = $0.50 per mile

b = $4 per ride

y = 0.5x +4

b. Carla’s Cabs does not charge a fixed rate but charges $1.00 per mile.

m  = $1 per mile

b = $0 per ride

y = x

The students in your class are going on a field trip. The ratio of teachers to students must be 1 to 7.
Which graph shows the number of teachers needed for 28 students?

Answers

Answer:

4 teachers for 28 students

Step-by-step explanation:

28/7 = 4

What is the center and radius of the circle with the given equation x^2 + y^2 + 14x - 12y +69 = 0

Answers

Answer:

Center is (7,-6)

Our radius is 4

Step-by-step explanation:

Subtract 69 to both sides

Complete the square of the x terms and y terms.

[tex] {x}^{2} + 14x[/tex]

[tex] {y}^{2} - 12y[/tex]

(To complete the square divide the coefficient by 2 and square it).

[tex] (\frac{14}{2} ) {}^{2} = 49[/tex]

[tex]( \frac{ - 12}{2} ) {}^{2} = 36[/tex]

Add those terms to the full equation. Add 36 and 49 to the right side as well

[tex] {x}^{2} + 14x + 49 + {y}^{2} - 12y + 36 = 16[/tex]

Simplify the x and y terms into a binomial.

[tex](x + 7) {}^{2} + (y - 6) {}^{2} = 16[/tex]

Set the left side equal to zero separately to find the center and take the square root of the right side to find the radius.

[tex]x + 7 = 0[/tex]

[tex]x = - 7[/tex]

[tex]y - 6 = 0[/tex]

[tex]y = 6[/tex]

[tex]16 = {x}^{2} [/tex]

[tex]4 = x[/tex]

So our center is (-7,6)

Our radius is 4.

(2) what is being cooked in a preserve cooker?​

Answers

Did you mean pressure cooker?

Answer:

Rice and other items are being cooked in pressure cookers

I hope it helps you

Gravel is being dumped from a conveyor belt at a rate of 15 ft3/hr and its coarseness is such that it forms a pile in the shape of an inverted right cone whose height is three times its base radius. How fast is the height of the pile increasing when the pile has a height of 10 ft

Answers

Answer:

0.43 ft/hr

Step-by-step explanation:

dv/dt = 15ft³/hr

Height = 10ft

We are required to get dh/dt

h = 3r

r = h/3

Formula for volume = 1/3πr²h

We put value of h

1/3π(h/3)²h

= 1/3π(h²/9)h

= 1/3πh³/9

= πh³/29

dv/dt = 1/27π.3h²dh/dt

= dv/dt = πh²/9dh/dt

Remember dv/dt = 15

When we put this in we get

dh/dt = 15x9/3.142x10²

= 135/314.2

= 0.43 ft³/hr

Please check the attachment I added also to add you.

Find the identical expression for the following plz show work

Answers

THAT IS A VIRUS DO NOT GO TO IT DONT GO TO ANY LINK THEY ALL ARD VIRUSES

Which expression correctly represents 10 times the difference of a number and six

Answers

Answer:

10(6 - x) or 10(x - 6)

Step-by-step explanation:

Let the number be x.

Answer: 10(6 - x) or 10(x - 6)

What is the area of this?

I need step by step

Answers

Answer:

Driveway Area = 218 square feetGarden Area = 230 square feetTotal Area = 448 square feet

See diagram below.

====================================================

Explanation:

Start at the lower left corner of the entire figure. Move 20 ft directly to the right until reach the end of the driveway at the bottom. Now move 10 ft up so you reach the other side of the driveway (the 26 ft side). In the process of moving 10 ft up, mark a new line segment. I've done so in red in the diagram below.

I've also drawn a green box. The red line and green box form a shape of a flag on a flagpole. The pole being 10 ft tall and the green box (flag) is a 6 by 3 rectangle. The 6 is from 26-20 = 6 and the 3 is from 10-7 = 3. Note how I'm subtracting the opposite side values to help figure out the dimensions of this green box.

The 10 ft by 20 ft portion of the driveway is 10*20 = 200 square feet. The green box adds on another 18 sq ft because 6*3 = 18. In all, we have 200+18 = 218 square feet for the driveway.

-------------------

If you want to know the area of the garden, then we first compute the overall area of everything shown. That's 32*14 = 448 square feet. Subtract off the driveway's area to get 448-218 = 230. Therefore, the garden's area is 230 square feet.

The mass of the Sun is about 2 × 10^27 metric tons, or 2 × 10^30 kilograms. How many kilograms are in one metric ton?

Answers

Answer:

[tex]\frac{2 * 10^{30} }{2 * 10^{27} } = 10^{3} kg[/tex]

MY TEAS GONE COLD I WONDERJNV WHY I GOT OUTTA BED ALONE HELP PLEASE

Answers

Answer:

54

Step-by-step explanation:

2/3(7-16)^2

2/3(-9)^2

2/3*81

54

2(3x - 32y) + 3(-2x - 4y)

Answers

the answer to this is > -76y

HHHEEELLLPPPPP MMMMMMEEEEEE!!!!!!

Which is the graph of the function g(x)=−x^2−4x−1?

Answers

Answer:

its a, the first one

Step-by-step explanation:

i graphed it have a good day (:

HELP it's Geometry HW I WILL GIVE BRAIN LIST AND 5 STARS​

Answers

Number one: if line segments SR & RT are perpendicular line segment Tu and US are perpendicular and angle STR is congruent to angle TSU, then triangle TRS is congruent to triangle SUT
Number two: if line segment AC is congruent to line segment CB and line segment CB bisects line segment AB, then < a is congruent to < B

jessica wondered if elementary school students tend to write more when they are given

Answers

full question plsAnswer:

Step-by-step explanation:

Work out the percentage change to 2 decimal places when a price of £200 is increased to £210.99.

Answers

Answer:

Let percentage be x%

According to the question

200+x%of 200=£210.99

X%of 200=£210.99-200

X/100×200=10.99

X=10.99/2=5.495% is required percentage.

Step-by-step explanation:

Which function could be represented by the graph on the
coordinate plane?

Answers

Answer:

where is the graph?

Step-by-step explanation:

What is the value of x

Answers

Answer:

180

Step-by-step explanation:

The value of x would be 180

Just wondering does anyway else do vava? 8th grade

Answers

Answer:

I have heard of it but I myself do not

Answer:

What's vava just wondering also your in 8th grade?

I need help on this question someone please help. x/4=-12 (this says x divided by 2 equals -8). Explain how you would solve for x and what you would get. I’m in 7th grade so can someone make it easy to read like at the explaining part thanks.

Answers

So since our first example is X/4=-12 the first step would be to multiply 4 to both sides meaning you would multiply 4 by the division of 4 so it cancels out because they’re opposite operations do the same to the -12, so -12x4=-36 x=-36 the other example would be the same multiply 2 to both sides so on the left it would cancel out and on the right it would be -16 which is the answer to x
Hope this could help at least a little

Can someone help me? I’ll reward points + brainalist

Answers

Answer:

The answer is B.

Answer:

b) A = π ([tex]5^{2}[/tex])

Step-by-step explanation:

area = π [tex]r^{2}[/tex]

diamter

⇒ 10

radius is half of the diameter

⇒ 10 ÷ 2 = 5

area = 3.14 × [tex]5^{2}[/tex]

How much will a shopper save on a TV that is on sale for 25% off the regular price of $399.99

Answers

Answer:

299.25

Step-by-step explanation:

Im pretty sure this is correct!!

Answer:

$100

Step-by-step explanation:

399.99 * 0.25 = 99.9975 (100)

399.99 - 100 = 299.99

$299.99 = Cost after discount

2) The number of rose blooms in Betty's garden is 24 more than the number of blooms in May's garden. There
are at least 135 rose blooms in Betty's garden. How many blooms are possible in May’s garden?

Answers

Answer:

There are at least 111 rose blooms in May's Garden.

Step-by-step explanation:

135-24 is 111 and Betty doesn't have a maximum of rose blooms so that means she can have an infinite amount but it also means that may can't have less than 111.

Please let me know if I am incorrect

Ignore the answer I chose it didn't let me click off of it

Answers

Answer:

d i think

Step-by-step explanation:

pretty sure it would be d

Help please thank uuuu

Answers

Answer:

B. x = 7; AB = 9, AC = 12

Step-by-step explanation:

12/4 = (x + 2)/(x - 4) (similar triangles theorem)

3 = (x + 2)/(x - 4)

Cross multiply

3(x - 4) = (x + 2)

3x - 12 = x + 2

Collect like terms

3x - x = 12 + 2

2x = 14

x = 14/2

x = 7

✔️AB = x + 2 = 7 + 2

AB = 9

✔️AC = (x + 2) + (x - 4) = (7 + 2) + (7 - 4)

AC = 9 + 3

AC = 12

Use the image to the right to answer the questions:
a. What theorems would/could you use to find x?
b. Find the value of x.
Thank you so much in advance! :)

Answers

Answer:

a. Linear pair theorem

b. x = 40

Step-by-step explanation:

a. You can use linear pair theorem. That is, two angles on a straight line are supplementary. They sum up to 180°

b. Thus:

x + (4x - 20) = 180°

x + 4x - 20 = 180

5x - 20 = 180

5x = 180 + 20

5x = 200

x = 200/5

x = 40

5/6 + (-4/9) - (-2), is this right??

Answers

Answer:

YES SIR OR I MEANT YES MAM

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