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Mathematics High School

A pair of fair dice is rolled once. suppose that you lose $ 8 if the dice sum to 3 and win $ 13 if the dice sum to 10 or 12. how much should you win or lose if any other number turns up in order for the game to be fair?

2 months ago

Solution 1

Guest #80

2 months ago

You should lose $1.20 for any other outcome to make it a fair game.

There are 2 ways to get a sum of 3 out of 36 outcomes; this probability is 2/36.
There are 4 ways to get a sum of 10 or 12 out of 36 outcomes; this probability is 4/36.
There are 36-(2+4) = 36-6 = 30 other outcomes out of 36; this probability is 30/36.

We lose $8 if we get a sum of 3; this expected value is -8(2/36) = -16/36.
We win $13 if we get a sum of 10 or 12; this expected value is 13(4/36) = 52/36.
Using x as the amount we win or lose for the other outcomes, the expected value is 30x/36.

In order to be a fair game, the amount we win and/or lose should come outto( $0 total.

Together we have the equation
-16/36+52/36+30x/36 = 0

Adding the fractions, we have
(-16+52+30x)/36 = 0
(30x+36)/36 = 0

Multiplying both sides by 36,
30x+36=0*36
30x+36=0

Subtracting 36 from both sides,
30x+36-36=0-36
30x=-36

Dividing both sides by 30,
30x/30 = -36/30
x=-36/30 = -1.2

Thus we should lose $1.20 for any other roll.

📚 Related Questions

Question

A quality control expert randomly samples 60 pairs of sunglasses and finds 5 defective pairs. predict how many defective pairs will be in a shipment of 420 sunglasses.

Solution 1

For this case the first thing you should do is find the percentage of sunglasses that are defective.

For this, we make the following rule of three:

60 pairs -------------------> 100%

5 pairs ---------------------> x

From here, we clear the value of x.

We have then:

$x = (\frac{5}{60}) * (100)\\x = 8.3%$

We now look for the amount of sunglasses that may come with defects.

We have then:

$N = (0.083) * (420)\\N = 34.86$

Rounding to the nearest whole number:

$N = 35$

Answer:

About 35 defective pairs will be in a shipment of 420 sunglasses

Solution 2

420/60=7
7*5=35 sunglasses

Question

If a storage tank that measures 12 feet by 9 feet by 8 feet is designed to store gas that costs $1.82 per cubic foot, what does it cost to fill the tank to one-half of its capacity?

Solution 1

For this case, the first thing to do is find the volume of the tank.
We have then:
V = (12) * (9) * (8)
V = 864 feet ^ 3
Then, the cost of filling half the tank is given by:
C = (1/2) * (1.82) * (864)
C = 786.24 $
Answer:
It costs to fill the tank to one-half of its capacity about:
C = 786.24 $

Question

I have milk that contains 1 percent fat and milk that contains 4 percent fat. a customer wants a double latte made with 1/3 of a pint of 2 percent milk. how much of each type of milk should i use ?

Solution 1

The double lathe milk with 2 percent fat concentration, is made by

considering the concentration and amount of each constituent.

The amount of each type of milk to be used in the $\dfrac{1}{3}$ pint of double lathe

are;

$\dfrac{2}{9}$ pint of the 1 percent fat milk and $\dfrac{1}{9}$ pint of the 4 percent fat milk.

Reasons:

Let x represent the amount of the milk that contains 1 percent fat in the

volume of the 2 percent fat milk.

Therefore, we have;

The amount of the 4 percent fat milk to be used = $\dfrac{1}{3} - x$

$Amount \ of \ fat = \dfrac{1}{100} \times x + \dfrac{4}{100} \times \left (\dfrac{1}{3} - x\right) = \dfrac{2}{100} \times \dfrac{1}{3} = \dfrac{2}{300}$

$\dfrac{1}{100} \times x + \dfrac{4}{100} \times \left (\dfrac{1}{3} - x\right) = \dfrac{4 - 9 \cdot x}{300} = \dfrac{2}{300}$

Therefore;

4 - 9·x = 2

4 - 2 = 9·x

$x = \dfrac{2}{9}$

The amount of the 1 percent fat milk to be used for the double lathe, x = $\dfrac{2}{9}$

of a pint.

The amount of the 4 percent fat milk to be used for the double lathe = $\dfrac{1}{3} - x$

Therefore;

The mount of the 4 percent fat milk = $\dfrac{1}{3} - \dfrac{2}{9} =\dfrac{1}{9}$

The amount of the 4 percent fat milk to be used for the double lathe = $\dfrac{1}{9}$

pint.

Learn more here:

brainly.com/question/13220698

Solution 2

You should use 2/9 of a pint of the 1% milk and 1/9 of a pint of the 4% milk.

Let x be the amount of 1% milk used. 1% = 1/100 = 0.01; this gives us 0.01x to represent this.

We know that we will use the 4% milk to make up the rest of the 1/3 pint; this gives us 0.04(1/3-x).

Together, they will make 1/3 pint of 2% milk, or 0.02(1/3)

This gives us the equation
0.01x+0.04(1/3-x) = 0.02(1/3)

Multiplying, we have
0.01x+0.04/3-0.04x = 0.02/3

We can multiply everything by 3 to eliminate the fractions:
0.01x*3 + 0.04 - 0.04x*3 = 0.02
0.03x + 0.04 - 0.12x = 0.02

Combining like terms, we have
-0.09x + 0.04 = 0.02

Subtract 0.04 from both sides:
-0.09x + 0.04 - 0.04 = 0.02 - 0.04
-0.09x = -0.02

Divide both sides by -0.09:
-0.09x/-0.09 = -0.02/-0.09

This gives us x = 2/9, so we will use 2/9 of a pint of the 1% milk.

1/3 - 2/9 = 3/9 - 2/9 = 1/9; we will use 1/9 of a pint of the 4% milk.

Question

An electrician can wire a house in 20 hours. if she works with an apprentice, the same job can be completed in 12 hours. how long would it take the apprentice, working alone, to wire the house?

Solution 1

We know that
An electrician can wire a house in ------------> 20 hours
so
100%----------------> 20 hours
X-------------------> 12 hour
x=12*100/20----> x=60%

that means
the apprentice in 12 hours complete the (100-60)----> 40%

the apprentice in 12 hours complete -------> 40%
x hours------------------------------------> 100%
x=100*12/40-----> x=30 hours

the answer is
30 hours

Question

A man has 25 25 coins in his pocket, all of which are dimes and quarters. if the total value of his change is $ 4.45 $4.45, how many dimes and how many quarters does he have?

Solution 1

If all were dimes, the value would be $2.50. The man has $1.95 more than that amount. Trading a dime for a quarter increases the value by $0.15, so there must be
$1.95/$0.15 = 13
quarters.

The man has 12 dimes and 13 quarters.

_____
Check:
12*$0.10 +13*$0.25 = $1.20 +3.25 = $4.45 . . . (answer checks OK)

Question

The sum of two numbers is 67 . The smaller number is 11 less than the larger number. What are the numbers?

Solution 1

Lets work this out...
67 is the answer we have so 67 - 11=56 so 56+11= 67
sum: addition
so 67 is a sum
Ans:56 + 11 = 67

Solution 2

Lets work this out...

67 is the answer we have so 67 - 11=56 so 56+11= 67

sum: addition

so 67 is a sum

Ans:56 + 11 = 67

Question

Find the measure of an angle between 0º and 360º coterminal with an angle of –110º in standard position

Solution 1

Answer:

An angle measures how how much you have to rotate one line called initial side so it lies on the top of other line called the terminal side. Angles whose vertex is located at the origin having the initial side on the positive x-axis is said to be in standard position. On the other hand, coterminal angles are angles in standard position having the same terminal side. In this way, for the angle:

$-110^{\circ} \\ \\ Its \ coterminal \ is: \\ \\ \alpha=360^{\circ}-110^{\circ}=\boxed{250^{\circ}}$

Question

The queston is find the equivalent fraction of 48/60 with the numerator 8 what is the answer?

Solution 1

$\frac{48}{60} = \frac{8\cdot6}{10\cdot 6} = \frac{8}{10} .$

Solution 2

the answer is is i have no absolute idea but i need points and it didn't let me copy the other guys answer.

Question

A researcher reports that mean ratings of liking for some food are m = 0.8, sd = 2.4. if the null hypothesis was that the mean equals 0, then what is the effect size for this test using estimated cohen's d?

Solution 1

cohen's d is a rathe rwrong way to word things so i suggest you rerun your Claulctaion

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A pair of fair dice is rolled once. suppose that you lose ​$ 8 if the dice sum to 3 and win ​$ 13 if the dice sum to 10 or 12. how much should you win or lose if any other number turns up in order for the game to be​ fair?

Solution 1

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A pair of fair dice is rolled once. suppose that you lose $ 8 if the dice sum to 3 and win $ 13 if the dice sum to 10 or 12. how much should you win or lose if any other number turns up in order for the game to be fair?