The Problem of the Points. Two players engage in a game. They are equally matched, and the chances of winning a point are the same for each player. The first player to score 10 points wins the $100 stakes. The game is interrupted suddenly when Player A has 7 points and Player B has 5 points. How should the stakes be divided fairly

Answers

Answer 1

Answer:

Player A receives $77.34375 of the sakes

Player B receives $22.65625 of the stakes

Step-by-step explanation:

Given that at the time the game was interrupted, we have;

The number of points player A  has = 7 points

The number of points player B has = 5 points

The amount the first player to score 10 points wins = $100

The number of points remaining for player A to win the game = 3

The number of points remaining for player B to win the game = 5

Therefore, the number of trials remaining for a winner to emerge = 3 + 5 - 1 = 7 trials

We take the probability that Player A wins a point as success

We find the likelihood of Plater A winning by using binomial theory as follows;

[tex]P(S) = \sum\limits_{j=3}^7 \dbinom{7}{3} \cdot \dfrac{1}{2^7} = \dfrac{35}{128} + \dfrac{35}{128} + \dfrac{21}{128} + \dfrac{7}{128} + \dfrac{1}{128} = \dfrac{99}{128}[/tex]

Therefore, given that the likelihood of Player A winning = 99/128

The stakes should be divided such that Player A gets 99/128 share of the stakes while Player B gets 1 - 99/128 = 29/128 share of the stakes

Therefore, Player A gets (99/128) × $100 = $77.34375

Player B gets (29/128) × $100 =  $22.65625


Related Questions

URGENT PLZ HELP

Find the measure of the arc or central angle indicated. Assume that lines which appear to be
diameters are actual diameters.

Answers

Answer:

Step-by-step explanation:

ok I forgot to tell you the arc PTR would be 126 +54 +14(4) +4 which equals 240 degrees. Answer.

solve the inequality 0<5x-2<8

Answers

Answer:

×= 2 this is what I got as a result to my equations

0 < 5x - 2 .......... (1)
5x - 2 < 8 .......... (2)

(1):
0 < 5x - 2

2 < 5x

2/5 < x

x > 2/5


(2):
5x - 2 < 8

5x < 10

x < 2

plssss help im stuck and this is worth 20 percent

Answers

Answer:

Percentile 2020 Percent Change

18%           $4,480.43 30.8%

19%      $5,378.37 24.0%

20%   $6,368.35 24.3%

21%         $7,363.47 22.4%

Step-by-step explanation:

A student multiplied the two polynomials below. Find the Errors:

a. Clearly state the two mistakes made by the student in their multiplication table.

b. State what the correct answer should be.

Answers

second one is correct    

Step-by-step explanation:

The diameter of a circle is 3 meters. What is the circumference?

Answers

Answer:

C≈9.42m

Using any of this formulas

C=2πr

C=2πrd=2r

Solution:

C=πd=π·3≈9.42478m

Answer the following. Round all answers to the nearest hundredths place.
The angle of elevation from point A to the top of the cliff is 38 degrees. If point A is 80 feet from the base of the cliff, how high is the cliff?

Answers

Answer:

62.5ft

Step-by-step explanation:

It doesnt matter if there's bumps along the side, the height will still reach to the same point.

Using trigonometry we have a adjacent and the opposite.

Hypotenuse is opposite the right angle

Opposite is opposite the angle

Adjacent is the last side to remain

Soh Cah Toa

We'll be using toa (Tan) because o and a (opposite and adjacent)

rearranging the original formuma :

Side × tan(Angle)

80 × tan (38) =62.50285....ft

choose all answers that apply​

Answers

Answer:

none of the above

Step-by-step explanation:

An isosceles trapezoid cannot be rotated to create the same image therefore it has no angle of rotational symmetry.

Anji bought 4 shirts for $56.80. She later bought a shirt for $19.20. What was the mean cost of all the shirts in dollars?

Answers

Answer:

$15.20

Step-by-step explanation:

When you are asked to find the mean, you would add up the costs of the shirts and then divide them by however many shirts she got.

56.80 + 19.20 = 76

76 ÷ 5 = 15.20

Thus the mean cost is $15.20

Hope this helped!

the pounds p of the flour and how many cakes c you can make

Answers

Answer:

How many pounds of flour do you have and how many pounds of flour it takes to make a cake?

Step-by-step explanation:

pls help I'll mark the first person brainliest answer all​

Answers

Answer:

4

a. 12

b. 8

c. 30

d. 40

Step-by-step explanation:

each exterior = 360/n

30*n=360

divide both side by 30

Answer is 12

The same apply to others to 4d

so first its 4

a. 12

b. 8

c. 30

d. 40

i will try to explain:

each exterior = 360/n

30*n=360

divide both side by 30

Answer is 12

The same apply to others to 4d

A seller has a house that is 1800 square feet. The neighborhood comps show
the line of best fit to be y = 0.074x +50 48. What is a fair price for this house?
A. $150,000
B. $183.68
C. $150.00
D. $184,000
SUBMIT

Answers

A fair price for this house is $183.68. Therefore, option B is the correct answer.

What is the equation of a line?

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

Given that, a seller has a house that is 1800 square feet.

The neighborhood comps show the line of best fit to be y = 0.074x+50.48.

Substitute x=1800 in the given equation, we get

y=0.074×1800+50.48

y=$183.68

Therefore, option B is the correct answer.

To learn more about the equation of a line visit:

https://brainly.com/question/2564656.

#SPJ1

Giving out the brainlest answer !!! help plsss ASAP !!!!!!!

Answers

Answer:

5

Step-by-step explanation:

As given  

  1/sqrt2=x/5sqrt2

5sqrt2/sqrt2=x                Both sqrt will get cancelled

5=x

which is the following is true about the graph of linear inequalities?
a.)it is a line
b.)it is a parabola
c.)it os a curve
d.)it is a half-plane​

Answers

Answer:

d.) half-plane..

Reason:

A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥. The half-plane that is a solution to the inequality is usually shaded.

The product of five and a number plus 10 is at least thirty.

Answers

5+10+x is greater than or equal to 30 ( use the greater of equal to sign)

A jar contains 6 red jelly beans, 4 green jelly beans, and 4 blue jelly beans.
If we choose a jelly bean, then another jelly bean without putting the first one back in the jar, what is the
probability that the first jelly bean will be blue and the second will be blue as well?

Answers

First jellybean:4/14
Second jellybean:3/14

What is the equation of this trend line?
Enter your answers by filling in the boxes.
K= J+

Answers

Answer:

K = -2  J = 28

Step-by-step explanation:

I took the k12 test

Answer:

The answer is K=-2 J+24.

Step-by-step explanation:

Question 6 (5 points)
Which of the following statements is true for 6.24?
O A) It's irrational because 6.24 =
68/33
OB) It's irrational because 6.24 =
= 60/25.
OC) It's rational because 6.24 = 68/33.
OD) It's rational because 6.24 =
66/25.

Answers

Answer:

C

Step-by-step explanation:

it's rational because 6.24 can be 68/33

sorry if I'm wrong!!

the answer is c because 6.24= 68/33

What is the difference in the mean absolute deviation for the average temperatures ?

Answers

Answer:Mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean. Mean absolute deviation is a way to describe variation in a data set. Mean absolute deviation helps us get a sense of how "spread out" the values in a data set are.

Step-by-step explanation:

to the Pythagorean Theorem
Rapids
For the following right triangle, find the side length x.
20
21

Answers

Answer:

x = 29

Step-by-step explanation:

[tex]c^{2} = a^{2} + b^{2}[/tex]

[tex]c^{2} = 20^{2} + 21^{2}[/tex]

[tex]c^{2} = 400 + 441[/tex]

[tex]c^{2} = 841[/tex]

[tex]\sqrt{c^2} = \sqrt{841}[/tex]

[tex]c = 29[/tex]

As per the Pythagorean theorem, the value of 'x' for the given right angle triangle is 29.

What is the Pythagorean Theorem?

"The Pythagorean theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle ABC, in which we have BC² = AB² + AC²​​. Here, ​​​​AB is the base, AC is the altitude (height), and BC is the hypotenuse."

Given, the value of the three sides of the right angle triangle are 20, 21, and 'x'.

Here, x = the hypotenuse of the right angle triangle.

Therefore, using the Pythagorean theorem, we get:

x² = 20² + 21²

⇒ x² = 400 + 441

⇒ x² = 841

⇒ x = √(841)

⇒ x = 29 (ignoring the negative value of the square root)

Therefore, the value of 'x' is 29.

Learn more about the Pythagorean Theorem here: https://brainly.com/question/20545091

#SPJ2

Item 5
Which measure of central tendency best describes the data?

47, 47, 48, 54, 102, 45, 100, 48, 83


either mean or median

median only

mean only

Answers

Answer:

the answer is either mean or median because you can find both of them given the data

Help please!!!When the clock struck midnight, Cinderella ran 3 miles back to her house from the ball. How many yards did she run?

Answers

Answer:

she ran 5,280 yards

Step-by-step explanation:

Answer:

5280

Step-by-step explanation:

Well, there are 1760 yards in a mile, aka 5280 feet. (5280ft/3=1760yds). 1760x3=5280.  I hope this was an okay explanation, this is my first day on Brainly with an account, hehe.

(8x + 11x) + (-7 - 18)

Answers

Answer:

19x - 25

steps:

(8x + 11x) + (-7 - 18)

19x + (-25)

positive x negative = negative

19x - 25

Answer:

19x - 25

Step-by-step explanation:

(8x + 11x) + (-7 - 18) <------- add the bold ones (combine like terms)...

19x + (-7 - 18) <--------------- subtract the bold ones...

(19x) - 25 <-------------------- eliminate parenthases

19x - 25 <--------------------- solution...

1/3 as long as 6 meters meter(s) ??​

Answers

Answer:

1/3 of 6 meters is 2 meters

Step-by-step explanation:

what is the volume of a rectangular prism wi the the dimensions3 base 5/8 cm, height 2/3 cm, and length 3/4 cm?

Answers

Answer:

5/16 cm³

Step-by-step explanation:

Given that the:

Width (W) = 5/8 cmHeight (H) = 2/3 cmLength (L) = 3/4 cm

Find the volume of the cuboid!

Volume equation =

W × H × L =

5/8 × 2/3 × 3/4 =

(5×2×3)/(8×3×4) =

30/96 =

5/16 cm³

The volume = 5/16 cubic centimetres

____________________

#IndonesianPride - kexcvi

Arthur spends his salary of k3550 for food, clothing, recreation and savings, which are in the ratio of 48:20:15:37, respectively.How much does he spend for each category?​

Answers

k1704:k710:k532.5:k1,313.5

Branliest to correct answer explain how you solved it please

Answers

Answer:

0.03

Step-by-step explanation:

.25% for the tails times .5 for the odd number on the dice times 0.25 for the clubs because it is a 13/52 chance you will pull a clubs and put that all together and you get 0.03125 simplified and you get 0.03

Answer:

0.03

Step-by-step explanation:

The probability of landing on 1 tail is 1/2, since it is 1 out of 2 options, a tail or a head. If you want the probability of two tails, it would be 1/2 * 1/2 = 1/4.

Next we can take the probability of rolling an odd number on a fair die. A fair die has 3 even numbers: 2,4,6; and 3 odd numbers: 1,3,5. Since 3/6 or 1/2 of the numbers are odd, there is a 50% chance that it would roll an odd number.

Finally, drawing a club out of standard deck of cards is 1/4, since there are 4 choices: hearts, spades, clubs, or diamonds. You now get the idea, and you can figure out that the probability would be 1/4.

Our last step is to multiply all the answers we get, since to get all of them at once would lower your chances. 1/4 * 1/2 * 1/4 = 1/32 = 0.03125; rounded to 0.03.

Find the value of x to the nearest tenth! HELP ME!!!!!!!!!!!!! (PICTURE IS BELOW)

Answers

Answer:

11.4

Step-by-step explanation:

By Pythagoras Theorem:

[tex]x^{2} = {7}^{2} + ( {4}^{2} + {8^{2}}) \\ \\ x^{2} = 49+(16 + 64)\\ \\ x^{2} = 49+80\\ \\ x^{2} = 129 \\ \\ x = \sqrt{129} \\ \\ x = 11.3578167 \\ \\ x = 11.4[/tex]

What the person said 11.4

Which is equivalent to (–9n + 12)?

Answers

-3(3n+4)

Step-by-step explanation:

answer from mathematics education book

HELP PLS MIGHT GIVE BRAINLIST BUT ONLY IF 2 PEOPLE ANSWER!

Answers

Answer:

[tex](21in,30in)=>210in^2[/tex]

[tex](15in,18in)=>90in^2[/tex]

[tex](15in,30in)=>150in^2[/tex]

Step-by-step explanation:

Required

Match the expressions on the left with the right

(a) 21 in by 15 in

Calculate area

[tex]Area = 21in * 15in[/tex]

[tex]Area = 315in^2[/tex]

Multiply by [tex]1/3[/tex]

[tex]1-third = 315in^2 * \frac{1}{3}[/tex]

[tex]1-third = 105in^2[/tex]

Hence:

[tex](21in,15in)=>105in^2[/tex]

(b) 21 in by 30 in

Calculate area

[tex]Area = 21in * 30in[/tex]

[tex]Area = 630in^2[/tex]

Multiply by [tex]1/3[/tex]

[tex]1-third = 630in^2 * \frac{1}{3}[/tex]

[tex]1-third = 210in^2[/tex]

Hence:

[tex](21in,30in)=>210in^2[/tex]

(c) 15 in by 18 in

Calculate area

[tex]Area = 15in * 18in[/tex]

[tex]Area = 270in^2[/tex]

Multiply by [tex]1/3[/tex]

[tex]1-third = 270in^2 * \frac{1}{3}[/tex]

[tex]1-third = 90in^2[/tex]

Hence:

[tex](15in,18in)=>90in^2[/tex]

(d) 15 in by 30 in

Calculate area

[tex]Area = 15in * 30in[/tex]

[tex]Area = 450in^2[/tex]

Multiply by [tex]1/3[/tex]

[tex]1-third = 450in^2 * \frac{1}{3}[/tex]

[tex]1-third = 150in^2[/tex]

Hence:

[tex](15in,30in)=>150in^2[/tex]

Need help ASAP for exam!!!Solve for x. Just type the NUMBER with no spaces. It will be marked wrong if you don't. If you want to write a square root, for example square root of 5

Answers

Answer:

Step-by-step explanation:

Other Questions
On her first day of college, Ria decided to specialize in two subjects: philosophy and mathematics. Students in both fields were intimidating; they acted like they were already mathematicians and philosophers, even though they were just freshmen. However, most of the students dropped out over the years while Ria studied hard, graduated with honors, and become a well-known scholar in the philosophy of mathematics Which statement is most clearly a theme in this story?A. Mathematics is a universal language. B. Philosophy is the best career path. C. An identity must be earned, not chosen.D. People should be true to their dreams. CAN AYONE PLEASE HELP ME WITH MY HOMEWORK ILL MARK BAINLYIST This is the full question if you can please solve this its really important.A machine cuts three circles of the same size from a rectangular sheet ofmetal as shown. What will happen? (Newton's 1st Law Egg Drop) Of all the students enrolled in the school of arts who responded, approximately what proportion responded that they play video games? Select four of the following that would increase the magnetic field of an electromagnet Which quotation from the answer choices below demonstrates the use of commas with a nonessential element? a. Each time they caught a glimpse of an animal, Jan's mom would lower her voice while they watched for the animal to come into view. b. Then, just ahead, a deer and her baby, called a fawn, cautiously stepped right onto the trail in front of Jan and her mom. c. While the mother deer stopped and stated at Jan and her mom, she also was making sure her baby was safe. d. "Stay back here, Jan," she said quietly. Lupe,you should see the once in a lifetime bargain I found! raved Sonia What is the major cause of changes in gene expression? Greater Energy Systems recently reported $9,250 of sales, $5,750 of operating costs other than depreciation, and $700 of depreciation. The company had no amortization charges, it had $3,200 of outstanding bonds that carry a 5% interest rate, and its federal-plus-state income tax rate was 35%. In order to sustain its operations and thus generate sales and cash flows in the future, the firm was required to make $1,250 of capital expenditures on new fixed assets and to invest $300 in net operating working capital. 8. Refer to the data for Greater Energy Systems. What is the firm's free cash flow Which values are solutions to the inequality below?Check all that apply. Can anyone help me with these questions I need it to pass please help me please will give brainliest there is an example Part 1: Identify key features and graph a parabola from standard form.Answer the following questions to determine the key features of the parabola based on theequation shown, and then graph it.12(x + 3) = (y - 2)^2a) What is the axis of symmetry of the parabola? Explain how to determine this from the equation.(1 point)b) What is the vertex of the parabola? (1 point)c) What is the focus of the parabola? (2 points)d) What is the directrix of the parabola? (2 points)e) Sketch a graph of the parabola and label the vertex, focus, directrix, and axis of symmetry. (4 point 2 pointsThe arrow next to the fuel gauge symbol on the dash tellsyou which side of the car the fuel filler is on.O TrueFalse question, the highlighted part, and passage are in the picture, AND ANSWER TODAYand no links... they could have firewall breakers and/or viruses (two similar things but they do different stuff)(the highlighted part looks bolded in the photo but if you somehow cant tell which one it is, its the part where it says "Soaring fire that sways and sings")A) hyperboleB) personificationC) simileD) metaphor Entity001 And Project Please help me I'm really lost the language mostly responsible for the transition from Old English to Middle English was- -French -Anglo-Saxon -Italian -Spanish Find the area of the shaded polygonsPLS HELP ASAP!! 3 |a| +5 |b| if a = 2; b = 1WILL AWARD BRAINLIEST "The Norms and Notions of what is just is isn't always justice"In your own words, what is justice?