Felicia has a stack of 10 cards. Each card is labeled with a number in the range 1 through 10 and no two cards have the same number. She picks three cards at random from the stack and adds the numbers on the three cards. What is the expected value of the sum

Answers

Answer 1

Answer:

The expected value of the sum of three numbers chosen out of 10 numbers will be 16.5.

Step-by-step explanation:

Felicia has a stack of 10 cards with number 1,2,3,4,5,6,7,8,9,10

Selecting 3 cards out of 10

10C3 = 120

Now she picks three cards to look at their numbers and sum it up

The possible three numbers are

(1 2 3), (1 3 2), (2 1 3) ,(2 3 1), (3 1 2), (3 2 1) ,(1 2 4), (1 4 2), (2 1 4), (2 4 1),

(4 1 2)│(4 2 1), (1 2 5), (1 5 2)│(2 1 5), (2 5 1) ,(5 1 2), (5 2 1), (1 2 6), (1 6 2), (2 1 6), (2 6 1), (6 1 2) ,(6 2 1) ,(1 2 7), (1 7 2) ,(2 1 7), (2 7 1), (7 1 2), (7 2 1), (1 2 8), (1 8 2), (2 1 8) ,(2 8 1), (8 1 2) ,(8 2 1), (1 2 9), (1 9 2), (2 1 9), (2 9 1), (9 1 2), (9 2 1),

(1 2... …, (6 10 8), (8 6 10), (8 10 6), (10 6 8), (10 8 6), (6 9 10), (6 10 9), (9 6 10),

(9 10 6), (10 6 9), (10 9 6), (7 8 9), (7 9 8), (8 7 9), (8 9 7), (9 7 8), (9 8 7), (7 8 10),

(7 10 8), (8 7 10), (8 10 7), (10 7 8), (10 8 7), (7 9 10), (7 10 9), (9 7 10), (9 10 7),

(10 7 9), (10 9 7) , (8 9 10), (8 10 9), (9 8 10), (9 10 8), (10 8 9), (10 9 8)

Now we sum it all up so minimum sum can be 1+2+3 = 6 andthe maximum can be 8+9+10 = 27

Let S denote the sum of the three numbers that are chosen and P(S=k) denotes its probability

P(S=6)=1/120  

P(S=7)=1/120

P(S=8)=1/60

P(S=9)=1/40

P(S=10)=1/30

P(S=11)=1/24

P(S=12)=7/120

P(S=13)=1/15

P(S=14)=3/40

P(S=15)=1/12

P(S=16)=1/12

P(S=17)=1/12

P(S=18)=1/12

P(S=19)=3/40

P(S=20)=1/15

P(S=21)=7/120

P(S=22)=1/24

P(S=23)=1/30

P(S=24)=1/40

P(S=25)=1/60

P(S=26)=1/120

P(S=27)=1/120

Now adding all the sum in order to get the expected value

∑(K=6 to 27) k*P(S=k) = 33/2 = 16.5

Therefore the expected value of the sum is 16.5.


Related Questions

A reading teacher brought sets of different numbers of books for her class. She paid the same price for each book

Complete the table to show the number of books she bought or the price she paid
(Put your answers in the Order of a,b,c)

Answers

Answer:

A) $15

B) 8

C) $25

Step-by-step explanation:

Salvador bought 6 lbs of coffee for $18.66. What is the unit price per pound?

Answers

Answer:

$3.11

Step-by-step explanation:

It is given that,

Salvador bought 6 lbs of coffee for $18.66.

We need to find the unit price per pound.

The unit price per pound is calculated by dividing total cost by 6 as follows :

[tex]C=\dfrac{18.66}{6}\\\\=\$3.11[/tex]

Hence, the unit price per pound is $3.11

There are 2 answers for this
(Please use a comma to separate them)

Emma got 90% of the questions on her history test correct if she answered 27 questions correctly, how many questions did Emma get wrong?

There were (A) questions on the test so she got (B) questions wrong

Answers

Answer:

There were 30 questions on the test so she got 3 questions wrong.

Step-by-step explanation:

Given that:

Correct answers by Emma = 27

Percentage of correct answers = 90%

Let,

x be the total number of questions on test

90% of x = 27

[tex]\frac{90}{100}x=27[/tex]

[tex]0.9x=27[/tex]

Dividing both sides by 0.9

[tex]\frac{0.9x}{0.9}=\frac{27}{0.9}\\x=30[/tex]

There were 30 questions on the test.

Wrong answers = Total questions - Correct answers

Wrong answers = 30-27 = 3

Hence,

There were 30 questions on the test so she got 3 questions wrong.

Pete, Bryan, and Philip are cousins. Pete's age is one-third of Bryan and Philip is five years elder than Bryan. If the sum of the age of the cousins is 40, find the ages of each.

Answers

Answer: Philips age is 20. Bryans age is 15

Step-by-step explanation:

arithmetic sequence ​

Answers

Answer:

First, find the common difference for the sequence. Subtract the first term from the second term. Subtract the second term from the third term. Subtract the third term from the fourth term. To find the next value, add to the last given number.

Step-by-step explanation:

help me pleaseeeeeeeee

Answers

C. None of the x-values repeat.

Answer:

C is because it doesn't have any repeating x-values or y-values

Step-by-step explanation:

0 Help please!
If you know geometry please help!

Answers

Answer:

D

Step-by-step explanation:

It's an Icoseles triangle do the two bottom angles are equal. 50+ 50 = 100. All triangle angles add up to 180 so 180 - 100 = 80

Answer:

Option D - 80

Step-by-step explanation:

The triangle is an isosceles triangle, which means that two angles and sides are the same. That means that other side is also 50°. All the angles in a triangle add up to 180°. Since we know two of the angles, we should know what the angle x is. We can write it as 50 °+ 50° + x = 180°. You can add 50° and 50° to get 100°. Now you have 100° + x = 180°. Subtract 100° from both sides to get x = 80°.

Hope this helps! :)

Rick’s scores in his last 15 rounds of golf are 72, 80, 75, 84, 78, 72, 75, 68, 81, 74, 79, 70, 77, 83, and 72. If he scores an 80 on each of the next three rounds, which measure of center would increase more, the mean or median?

Answers

Answer:

The median increased more

Step-by-step explanation:

Given that:

Scores on last 15 :

72, 80, 75, 84, 78, 72, 75, 68, 81, 74, 79, 70, 77, 83, 72

Obtaining the range, mean, median and mode from the data above :

Rearranged data:

68, 70, 72, 72, 72, 74, 75, 75, 77, 78, 79, 80, 81, 83, 84

Range = 84 - 64 = 16

Mode = 72 - frequency of 3)

Mean = ΣX / n where n = sample size

Mean = 1140 / 15 = 76

Median = 0.5(n+1)th term = 0.5(16)th term =

8th term = 75

A score of 80 on each of next 3 rounds :

72, 80, 75, 84, 78, 72, 75, 68, 81, 74, 79, 70, 77, 83, 72, 80, 80, 80

Rearranged data:

68, 70, 72, 72, 72, 74, 75, 75, 77, 78, 79, 80, 80, 80, 80, 81, 83, 84

Range = 84 - 68 = 16

Mean = ΣX / n where n = sample size

Mean = 1380 / 18 = 76.67

Median =0.5(n+1)th term = 0.5(19)th term =

9.5 = (9th term +. 10th term) / 2 = (77 +78) / 2 = 77.5

How many board feet of lumber would you have if you had 5 pieces of 4"x 2 points
4" X 8'?*

Answers

Answer:

6

Step-by-step explanation:

How to find inequalities

Answers

Answer:

Step 1 Eliminate fractions by multiplying all terms by the least common denominator of all fractions.

Step 2 Simplify by combining like terms on each side of the inequality.

Step 3 Add or subtract quantities to obtain the unknown on one side and the numbers on the other.

Hope that helped happy holidays!

Fine the values of x and y. Please explain .

Answers

.hhdjekekeke kekelekwkwkwkww

The stock of Company A gained $1.86 throughout the day and ended at a value of $94.86. By what percentage did the stock rise

Answers

Answer:

tTe answer is 1.96%

Step-by-step explanation:

given data

change in price/gain= $1.86

the closing price = $94.86

Required.

The percent rise.

Step two:

The formula for the percent rise is

=change/close price*100

substitute our given data

= 1.86/94.86*100

=0.0196*100

=1.96%

The day after a protest held by an employee's union, 32 out of 40 employees did not show up for work at the shoe factory, Which represents the percent of the employees who did show up for work the day after the protest?​

Answers

Answer:

Step-by-step explanation:

32 out of 40 did not show

8 out of 40 did show

When you ask "What is 8 out of 40?" you want to know what percent 8 is out of 40.

Here are step-by-step instructions showing you how we calculated 8 out of 40 as a percentage:

The first step is to divide 8 by 40 to get the answer in decimal form:

8 / 40 = 0.2000

Then, we multiplied the answer from the first step by one hundred to get the answer as a percentage:

0.2000 * 100 = 20.00%

Answer:

20 %

Step-by-step explanation:

What is 2,356 divided by 27​

Answers

Answer:336.57

Step-by-step explanation:

Answer:

87.259.

Step-by-step explanation:

What equation does this map show?

Answers

Answer:

Oh, it's y=3x-4.

Because it's slope is 3 and it crosses through -4 on the y axis, we know that that would be the equation.

Good luck with the assignment man, let me know of anymore questions. :)

Q#1 Pleaseeee answer my guy it’s literally the biggest grade I got and I’m tiredddd

Answers

Answer:

x < -15

Step-by-step explanation:

x/-5 > 3

x > 3 * (-5)

x > -15

can you put your tongue in a not??

Answers

Answer:

No, it is physically impossible to put your tongue in a knot.

Step-by-step explanation:

4(5a + 3) = 20a + 12 represent which property of multiplication?

Answers

Answer:

Distributive property of multiplication

Step-by-step explanation:

The distributive property of multiplication is basically distributing the terms outside the bracket to all the terms inside the bracket. In this case, 4 is multiplied to 5a as well as 3.

Helpppppppppppppppppp

Answers

Answer:

ik that problem gimmie a sec

Step-by-step explanation:

Step-by-step explanation:

since 1 and 2 are same the lines which create 1(g and p) and 2(h and r)

the lines g h and p r shoul be parallel. we also know that g h is parallel which proves that p and r should be parallel as well

which equation is equivalent to y= Ax + By = C

Answers

Answer:

slope intercept form

Step-by-step explanation:

that's what ax + by = c is

xoxo, your highness...

A chemist has 100 ml of 25% acid solution. how much of the solution does she need to drain and replace with 70% acid solution to obtain 100 ml of 60% acid solution?

Answers

Answer:

The proportion of acid at 70% that the chemist must use will be 77.8%, while the remaining 22.2% will be acid at 25%.

Step-by-step explanation:

Since the chemist has 100 ml of solution with 25% acid, and wants to obtain a solution of 60% acid by mixing the first with another 70% acid solution, to determine how much of each solution the chemical should use necessary to perform the following calculation:

70 x 1 + 25 x 0 = 70

70 x 0.9 + 25 x 0.1 = 65.5

70 x 0.8 + 25 x 0.2 = 61

70 x 0.7 + 25 x 0.3 = 56.5

Therefore, the proportion to be used is between 70% and 80% of acid at 70%, and 20% to 30% of acid at 25%.

70 x 0.75 + 25 x 0.25 = 58.75

70 x 0.76 + 25 x 0.24 = 59.2

70 x 0.77 + 25 x 0.23 = 59.65

70 x 0.78 + 25 x 0.22 = 60.1

Thus, the proportion should be between 77 and 78% of acid at 70% and 22 and 23% of acid at 25%.

70 x 0.778 + 25 x 0.222 = 60.01

Thus, finally, the proportion of acid at 70% that the chemist must use will be 77.8%, while the remaining 22.2% will be acid at 25%.

Which translation moves point Z so that the whole image is only in quadrant 1 and 2
Captionless Image

Answers

Answer:

I can’t see the picture!

Step-by-step explanation:

Find the exact value of cos(a-b) given sin(a)=-4/5 and cos(b)=-5/8 for a in Quadrant III and B in Quadrant II.

See picture for answer choices.

Answers

Answer: B

Step-by-step explanation:

Peter rolls 2 fair dice and adds the results from each.

Work out the probability of getting a total of 11.

Answers

Answer:

5/12

Step-by-step explanation:

im finding answers for hegarty maths and i got it wrong and it said 5/12 was the answers

thank me later

Answer:

2/36

Step-by-step explanation:

i found it on another website

Someone please help me !!!!!

Answers

It is 3.2 I believe
It’s 2.9 bc it’s 11 numbers

Round to the nearest whole number and cluster to give an estimate for 15.23 + 12.8 + 4.93 + 7.21.

Answers

Answer:

the answer is 40

Step-by-step explanation:

15.23+12.8+4.93+7.21=40.17 then you round 40.17 to 40

Answer:

40

Step-by-step explanation:

15.23 + 12.8 + 4.93 + 7.21

27.31 + 12.34

39.65

round the number to a whole number

40

13.
WRITE Math Write a word problem that involves two fractions.
Include the solution.
Please help fast

Answers

Answer: If you have 2/3 cup of water and 3/5 cup of oil, how huch liquid do you have in total?

1 and4/15

Step-by-step explanation:

Any help please I appreciate it

Answers

Answer:

12

Step-by-step explanation:

18-6

True or false:triangle angle some theorem is when all of them interior (inside)angles of a triangle add up to 180°?

Answers

True a triangle equals 180°

Answer:

true

Step-by-step explanation:

The sum of interior angles is 180 degrees (Triangle Angle Sum Theorem). All interior angles of a triangle are more than 0° but less than 180°. The bisectors of all the three interior angles intersect inside a triangle at a point called the in-center, which is the center of the in-circle of the triangle.

Trevor was reading a book for a book report. Last week, he read 35 pages of the book. This week, he read 4.5 times as many pages as he read last week.

How many pages of the book has Trevor read this week? Complete the explanation.

I only need like a
35
x 4.5
---------------
[ ]
[ ]
---------------
[ ]

Answers

9514 1404 393

Answer:

  see below

Step-by-step explanation:

Multiply the numbers as though they were integers, then mark off a number of decimal places in the product equal to the total number of decimal places in the numbers being multiplied (1).

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