A friend offers to play a game, in which you roll 3 standard 6-sided dice. If all the dice roll
different values, you give him $1. If any two dice match values, you get $2. What is the expected value of this game?

Answers

Answer 1

Answer: The expected value is $0.32

Step-by-step explanation:

The expected value can be calculated as:

EV = ∑xₙ*pₙ

Where:

xₙ is the n-th event.

pₙ is the probability of the n-th event.

First, let's see the events in this situation and the probability of each event.

Lossing $1.

This happens when you roll all different numbers.

To calculate the number of combinations where you roll all different values, we first need to count the number of possible options for each roll, this is:

First dice: you have 6 options

Second dice: You have 5 options, because we remove the option that was rolled in the first dice.

Third dice: You have 4 options, because we removed the two outcomes showed in the two previous rolls.

Then the number of combinations is:

c = 6*5*4 = 120.

And the total number of combinations for rolling 3 dice is equal to the product between the number of outcomes for each dice, each dice has 6 possible outcomes, then the total number of outcomes is:

C = 6*6*6 = 216

The probability of rolling all different numbers will be equal to the quotient between the number of combinations where you roll all different values and the total number of combinations:

P₁ = 120/216 = 0.56

In the other case, where you roll at least two equal outcomes, you win $2.

The probability for this case will be the complement of the previous one, then the probability can be calculated as:

P₂ = 1 - P₁ = 1 - 0.56 = 0.44

Then the expected value will be:

EV = -$1*0.56 + $2*0.44 =  $0.32

The expected value is $0.32


Related Questions

The answer to my question.

Answers

Answer:

145°

Step-by-step explanation:

As per the given information: quadrilateral ABCD is a parallelogram.

[tex] m\angle B + m\angle DCB =180\degree \\[/tex]

(adjacent angles of a parallelogram)

[tex] 110\degree + m\angle DCB =180\degree \\

m\angle DCB =180\degree - 110\degree \\

m\angle DCB =70\degree\\

m\angle DCG=\frac{1}{2} m\angle DCB \\(\because GC \: bisects \: \angle DCB) \\

m\angle DCF=\frac{1}{2}\times 70\degree... (\because C-G-F) \\

m\angle DCF=35\degree\\

m\angle BFC = m\angle DCF = 35\degree\\ (Alternate \: \angle s) \\\\

m\angle BFC + m\angle CFA = 180\degree\\ (straight \: line \: \angle s) \\\\

35\degree + m\angle CFA= 180\degree\\

m\angle CFA = 180\degree-35\degree \\\\

m\angle CFA= 145\degree \\\\

\huge\purple {\therefore m\angle GFA = 145\degree} \\(\because C-G-F) \\[/tex]

0.095-20/5=
Write it as a decimal

Answers

Answer:

-3.905

Step-by-step explanation:

0.095 - 20/5

0.095 - 4

-|4-0.095|

-|3.905|

-3.905

-3.905 is the awnser

solve for x and y :
9 + 12i = 3x + 4yi

Answers

Answer:

27

Step-by-step explanation:

At a football match, 10 men bought either a pie or a cup of
coffee. A pie costs 60p and a coffee costs 50p. The total
amount spent on pies and cups of coffee was £5.80. How many
of each must have been bought? (show all your working)​

Answers

Answer:

8 pies and 2 coffees

Step-by-step explanation:

10 men bought pie or a cup of coffee.

x=pie

y=coffee

x+y=10

0.6x+0.5y=5.8

0.6x+0.6y=6

0.1y=0.2

y=2

x=8

Hope this helps plz hit the crown :D

You have 15 marbles in a bag; 5 are red. If you pull out five marbles in a row and don't put
them back in, what are your chances of pulling all 5 red marbles? Decimal answer please.

Answers

Step-by-step explanation:

0.33 so says my mother bc she divide

Answer:

The probability of drawing a different marble is 0.25. The probability of drawing a red marble = 0.5

I do not know if this is correct please forgive me if I am wrong.

If I am right hope this helps!

If P is the circumcenter of triangle ABC, find each measure.
Find AP.
B
11x – 14
D
E
А
F
С
6x + 1

Answers

Answer:

Step-by-step explanation:

Hhhh

Answer: 19

Step-by-step explanation:

Did it

Two adjacent sides of a parallelogram are 7cm and 10cm respectively.Find its perimeter​

Answers

Answer:

Step-by-step explanation:

Perimeter=2(10+7)

=2(17)

=34cm

Chris bought c tickets to a movie for $8 each. Michele bought m tickets to a movie for $8 each. Which expression can be used to find the total amount Chris and Michele spent for these tickets?

Answers

Answer:

8c+8m

Step-by-step explanation:

c tickets are $8 a piece and m tickets are also $8 a piece. as an expression, the equation is not completed and cannot be completed until we know the value of the missing variables. to find the total, you must add the total amount of tickets Chris bought for 8 dollars and add that to the total of tickets Michele bought for 8 dollars

3. Lunch
Steven owns a restaurant that specializes in steak burgers! 4 burgers and 3 fries cost $24.50. If a burger costs $5, how much is each order of fries?


LET X =


EQUATION:






5. Dinner
The restaurant is full! There are some four-person tables and 8 tables with couples. If there are 56 people here, how many four-person tables are there?

LET X =


EQUATION






7. Dessert
Stuart’s bought a cake and 6 servings of ice cream. The cake was $12 and the total bill was $33. How much was each order of ice cream?

LET X =


EQUATION

Answers

Step-by-step explanation:

3)

4(5)+3x=24.50

20+3x=24.50

-20        -20

3x=4.50

/3      /3

x=$1.50

5)

4x+2(8)=56

4x+16=56

   -16   -16

4x=40

/4    /4

x=10 tables

7)

1(12)+6x=33

12+6x=33

-12        -12

6x=21

/6    /6

x=$3.5

The answer for part (3) is $1.5 each fry, answer for part (5) is 10 four-person table, and answer for part (7) is $3.5 each order of ice cream.

What is linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

3)

Let x be the cost of each fry.

4×5 + 3x = 24.50

20 + 3x = 24.50

3x = 4.5

x = $1.5 each fry

5)

Let x be the number of tables for a four-person.

Couple means two persons.

56 - 2×8 = 4x

4x = 40

x = 10 four-person tables

7)

Let x be the cost of each order of ice cream:

12 + 6x = 33

x = $3.5 each order of ice cream.

Thus, the answer for part (3) is $1.5 each fry, answer for part (5) is 10 four-person table, and answer for part (7) is $3.5 each order of ice cream.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ2

The length of a rectangle is twice its width. Find its area, if its perimeter is 7 1/3 cm.

Answers

Answer:

241/81 cm^2

Step-by-step explanation:

[tex]2\: lenghts = wide\\\\lenght=x\\\\2x=wide\\\\Perimeter = 2(wide+lenght)\\\\P=2(2x+x)\\\\P=2(3x)\\\\P=7\frac{1}{3}\\\\\frac{22}{3}=6x\\\\x=\frac{22}{3*6}\\\\x=\frac{11}{9}\\\\width = 2x=2(\frac{11}{9})=\frac{22}{9}[/tex]

[tex]Area = lenght\times width\\\\Area = \frac{11}{9}\times\frac{22}{9}\\\\A=\frac{11*22}{9*9}\\\\A=\frac{242}{81}cm^2[/tex]

Answer:

[tex]2\frac{80}{81}[/tex] cm²

Step-by-step explanation:

A = lw

P = 2(l + w)

~~~~~~~~~~~

l = 2w

2(2w + w) = [tex]7\frac{1}{3}[/tex]

2(3w) = [tex]\frac{22}{3}[/tex]

3w = [tex]\frac{11}{3}[/tex]

w = [tex]\frac{11}{9}[/tex]

l = [tex]\frac{22}{9}[/tex]

A = [tex]\frac{22}{9}[/tex] × [tex]\frac{11}{9}[/tex] = [tex]\frac{242}{81}[/tex] = [tex]2\frac{80}{81}[/tex] cm²

3x-(8x+4)=
pppppppppppppppppppppppllllllllllllllllllssssssssss

Answers

Answer:

-5x+4???

Step-by-step explanation:

I DON'T KNOW I'M SORRY

Answer:

-5x - 4

Step-by-step explanation:

3x - (8x + 4)

3x -8x -4

-5x - 4

A family went to a restaurant. The total cost of the meal was $48.30. The family had a coupon for 20% off the total. What was the final cost?​

Answers

Answer:

$38.64

Step-by-step explanation:

to find the percent off of the original price, multiply 48.30 to 20. then, move the decimal over twice.

48.30

x 20

----------

966    --------->       $9.66 off

then subtract that from 48.30.

$38.64 is you answer.

give me brainliest

WILL GIVE BRAINLIEST

Answers

One solution. I solved for X and it’s 28

Answer: x = 28

Step-by-step explanation:  

Trust me :)

Your friend finds the measure of the exterior angle shown. Is your friend correct?

Answers

Answer:

will i think that's true

Step-by-step explanation:

I hope this helps you

Answer:

I think that it is yes

Step-by-step explanation:

Hope this helped have an amazing day!

Free fall reaches 216km per hour. What is rate in meters per second.? How many meters fall during 20 seconds free fall?

Answers

Given,

Rate of free fall = 216 km/h

Solution,

km/h to m/s is converted as follows :

[tex]216\ \dfrac{km}{h}=216\times \dfrac{1000\ m}{3600\ s}\\\\=60\ m/s[/tex]

So, the rate of fall is 60 m/s.

If t = 20 s

Assume, initial velocity = 0

It will move under the action of gravity.

Using equation of motion,

[tex]h=ut+\dfrac{1}{2}gt^2\\\\h=0+\dfrac{1}{2}\times 10\times 20^2\\\\h=2000\ m[/tex]

Hence, this is all for the solution.

2a. A bicycle is $85. The tax is 6%. How much is the tax?
7

Answers

Answer = $5.10
85 x 0.06 = $5.10

Select the statement that indicates that the triangles in each pair are congruent.
50 points

Answers

Answer:

D. ∆XVW ≅ ∆XBC

Step-by-step explanation:

Angle X = Angle X (vertical angles are congruent)

Angle V = angle B (corresponding angles are congruent)

Angle W = angle C (corresponding angles are congruent)

The three angels in ∆XVW are congruent to the three corresponding angles in ∆XBC.

Therefore, the statement that indicates both triangles are congruent is:

∆XVW ≅ ∆XBC

Please help!!!!!!!!!

Answers

Answer:

$42.75

Step-by-step explanation:

18.80+23.95=$42.75

$42.75 I think sorry if I’m wrong

Write an expression for 2 times the difference of 8 and d

Answers

Answer:

2(8-d)

Step-by-step explanation:

16 - 2d

Answer:

2 x (8 - d)

Step-by-step explanation:

2 times means multiply by 2

difference of 8 and d means 8 minus d → 8 - d

Find the area round to the nearest 10th if necessary

Answers

Answer:

5th

Step-by-step explanation: because its the half and the closest area of the figure

64 + 112 + 290 = 466

5/6=1/3+d

Thank you for the help and have a good day :)

Answers

Answer:

d = 1/2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define

5/6 = 1/3 + d

Step 2: Solve for d

Subtract 1/3 on both sides:                    5/6 - 1/3 = dRewrite fraction:                                     5/6 - 2/6 = dSubtract:                                                  3/6 = dSimplify:                                                   1/2 = dRewrite:                                                    d = 1/2

Ask any question. i gottu

Answers

Answer:

why?

Step-by-step explanation:

Answer:

..is cereal a soup?

Step-by-step explanation:

is it tho?

1.) Name the corresponding
sides and angles.

Answers




Corresponding sides:
EF, HI
FG, IJ
EG, HJ
Corresponding angles:

200 people purchase a lottery ticket. Three winning tickets will be selected at random. If first prize is $100, second prize is $50, and third prize is $5, how many ways can the prizes be awarded?

Answers


EEEEEEEEeeEeeEeEeeEeEeE

Type the correct answer in each box. Use numerals instead of words.
Renee and David plan to file taxes as married filing jointly. They have a combined taxable income of $51,325. Use the table to determine the amount of tax due, and calculate their effective tax rate, rounding to the nearest tenth.

Answers

Answer:

the answer is 6766 and the percent is 13.2

Step-by-step explanation:

100 on the plato test

What is the solution to the rational equation x over x squared minus 9 plus 1 over x minus 3 equals 1 over 4x minus 12? (1 point)

Answers

Step-by-step explanation:

x²/(x²-9) + 1/(x-3) = 1/(4x-12)

4x² + 4(x+3) = 1

4x² + 4x + 11 = 0

Since the discriminant is negative, there are no real solutions.

The distance from Greg's house to Tanya's house is 7/10 of a mile. Which number correctly shows the number of miles a decimal?* Greg's house C Tanya's house Homile mile 07.10 7.0 0.7 0.07​

Answers

Answer:

7 divide by 10=0.7 so 0.7 is the correct answer

Georgette has purchased award plaques for her company’s conference. Each plaque
costs $7.50, and Georgette paid a one-time shipping fee of $40 for the order. Calculate the total cost for the order based upon the number of plaques purchased.

i need the slope

Answers

Answer:

y=1/7.50x+40

Step-by-step explanation:

I doubled checked myself on desmos and it worked. You start at 40$ because you pay that no matter what. For each one they buy the price goes up by 7.50$.

A typical credit card company charges 18% annual interest,
compounded monthly, on the unpaid balance. If your current balance is
$520 and you do not make a payment for 6 years, how much will you
owe? Answer rounded to the whole number

Answers

Answer:

$1,519

Step-by-step explanation:

Given that :

Balance = principal = $520

Time (t) = 6 years

Annual. Interest rate (r) = 18% = 0.18

Using the compound interest formula:

A = P(1 + r/n)^nt

n = number of times interest is applied per period ; A = final amount

Since interest is compounded monthly, n = 12

A = 520(1 + 0.18/12)^(12 * 6)

A = 520(1 + 0.015)^72

A = 520(1.015)^72

A = 520(2.9211579)

A = 1519.0021

Hence, final amount = $1519

What is the equation relating x and
y together?
X
10
15
20
25
30
y=[?]x +

Answers

You didn’t provide enough information
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