1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ololo11 [35]
3 years ago
9

A pair of fair dice is rolled once. Suppose that you lose ​$8 if the dice sum to 10 and win ​$11 if the dice sum to 11 or 12. Ho

w much should you win or lose if any other number turns up in order for the game to be​ fair?
Mathematics
2 answers:
KATRIN_1 [288]3 years ago
6 0
First find the possible dices rolls that give you 10, 11, and 12

Gives 10:
5,5
4,6
6,4

Gives 11 or 12:
5,6
6,5
6,6

The dice rolls have 6 * 6 = 36 possible combinations

The probability of getting a 10 is 3/32
The probability of getting an 11 or 12 is 3/32

multiplying those probabilities together with their reward/loss we have:

3/32 * -8 = -3/4
3/32 * 11 = 33/32

to make the game "fair" we need the probable amount of money you can win to be $0, so we can use the equation

-3/4 + 33/32 + (32/32 - 6/32)*x = 0

then you can just solve for x

HACTEHA [7]3 years ago
5 0

Answer:

Loss of $ 0.3.

Step-by-step explanation:

Since, when two dices are rolled,

Then the all possible outcomes = 36,

Also, the possible way of getting the sum of 10 are,

(4, 5), (5, 4), (5, 5),

So, the possibility of getting the sum of 10 = \frac{3}{36}=\frac{1}{12}

Now, the possible way of getting the sum of 11 or 12 are,

(5, 6), (6, 5), (6, 6),

So, the possibility of getting the sum of 11 or 12 = \frac{3}{36}=\frac{1}{12}

Now, the possible number of ways of getting other number= 36 - 3 - 3 = 30,

Thus, the possibility of getting other number = \frac{30}{36}=\frac{5}{6}

Given, for getting the sum of 10 profit is -$ 8, for the sum of 11 or 12 the profit is $11,  ( '-' sign shows the loss )

Let x be the profit of getting other number,

So, the expected value of the game = \frac{1}{12}\times -8+\frac{1}{12}\times 11 + \frac{5}{6}\times x

=-\frac{8}{12}+\frac{11}{12}+\frac{5x}{6}

If the game is fair,

Expected value of game = 0

\implies -\frac{8}{12}+\frac{11}{12}+\frac{5x}{6}=0

\frac{3+10x}{12}=0

3+10x=0

x=-0.3

Hence, there should be a loss of $ 0.3 if any other number turns up in order for the game to be​ fair.

You might be interested in
Two customers went to a post office to buy posicaids and large enkelapes Fast posrcard
Setler [38]
The answer to this question is A $1.42 because the first customer paid $12 for 14 postcards
3 0
3 years ago
4(x+9)=8x-7<br> Solve for x
valentina_108 [34]

Answer:

x = 10.75

Step-by-step explanation:

4(x+9)=8x-7

Step 1: Distribute the 4 to the x and 9

4 * x = 4x

4 * 9 = 36

We now have 4x + 36 = 8x - 7

Step 2: add 7 to both sides

36 + 7 = 43

-7 + 7 cancels out

We now have 4x + 43 = 8x

Step 3 subtract 4x from both sides

4x - 4x cancels out

8x - 4x = 4x

We now have 4x = 43

step 4 divide both sides by 4

4x / 4 ( the 4s cancel out and we're left with x )

43/4 = 10.75

We're left with x = 10.75

3 0
2 years ago
WILL GIVE BRAINLIEST!
Brrunno [24]

Answer:

The graph is not a function of x because x=0 intersects the graph at two points.

Step-by-step explanation:

The vertical line test is when you draw, well, a vertical line through the graph. the slope of a vertical line is undefined, and the formula written as x=_. So we can eliminate the choices with y=_.

We can clearly see that this graph isn't a function, so we can eliminate the answer choices that say that the graph is a function.

Just in case, draw a line at x=0, to check that it does indeed cross the graph in 2 places.

5 0
3 years ago
A hobby store is having a promotion on picture frames: buy 3 get the 4th frame at 75% off.
babunello [35]
3x + (x - 0.75x)
4x - 0.75x
x= cost of the frame
5 0
2 years ago
Which of the following is a polynomial?
Tcecarenko [31]

Answer:

(D.) 3x^2 + 6x

Step-by-step explanation:

the other options aren't complete and some don't even create a parabola.

3 0
2 years ago
Other questions:
  • Tickets to a concert cost $2 for children, $3 for teenagers and $5 for adults. When 570 people attended the concert, the total t
    5·2 answers
  • BRAINLIEST!!!<br> 2. Evaluate the logarithmic expression.
    5·1 answer
  • Plz answer me will mark as brainliest <br><br>solve - 3x + ( - 5y) - (-10) - 7x​
    6·1 answer
  • Zachary invested $5,300 in an account paying an interest rate of 9 % compounded
    15·1 answer
  • Plz help! Giving a lot of points! :)
    9·2 answers
  • Which equation is y +5 = 1/3 (x - 9) in slope-intercept form
    14·1 answer
  • 1. Are these two lines parallel, perpendicular or neither?
    13·1 answer
  • Q6. The diagram shows that a ship sails 34 nautical miles from its port. Then after sailing 19 nautical miles due east, it is di
    12·1 answer
  • Kerri has a germen shepherd that has a mass of 30,000 grams. how many kilograms is 30,000 grams
    15·1 answer
  • Finding the area of a regular polygon​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!