At a casino, people line up to pay $20 each to be a contestant in the follow- ing game: The contestant flips a fair coin repeatedly. If she flips heads 20 times in 20 mil a row, she walks away with lion dollars; otherwise she walks away with R 0 dollars
(a) Find the PMF of R, the reward earned by the contestant.
(b) The casino counts "losing contestants who fail to win the 20 million dollar prize. Let L equal the number of los- ing contestants before the first winning contestant. What is the PMF of L?
(c) Why does the casino offer this game?

Answers

Answer 1

Answer:

a)

P ( R = 20 million ) = 0.00000095367

P ( R = 0 million )  i.e. not winning = 0.99999904633

b)  P ( L ) = ( 1 - p )^l  * p

C)The casino offer the game because  the expected revenue exceeds the winning

Step-by-step explanation:

P( winning ) = P ( getting 20heads in a row ) = 0.5^20 = 0.00000095367

a)  PMF of R

P ( R = 20 million ) = 0.00000095367

P ( R = 0 million )  i.e. not winning = 0.99999904633

b) what is the PMF of L

L = number of loosing clients before winning

P( L = 0 ) = P   i.e. if first contestant wins, if the second contestant win, L=1 repeat same process continuously

P ( L = 2 ) = ( 1 - p)^2 p

Hence the PMF of L  

P ( L ) = ( 1 - p )^l  * p     where p = 0.5^20

C) The casino offer the game because  the expected revenue exceeds the winning

we can prove this using  the relation below

E( L ) =  ( 1 - P ) / 1 - ( 1 - P )

        = 1 / P - 1

where  p = 0.00000095367  ( probability of winning )

Hence E ( L ) = 1048575

hence expected revenue before someone wins

= (1048575 + 1 ) * 20 = $20,971,520


Related Questions

The circle graph shows Lenora's activities
during 10 hours at school.
School Activities
Homeroom 7.5%
Newspaper
7.5%
Gym
10.0%
Academic
Classes
50.0%
Lunch 5.0%
Softball
Practice
20.0%
How many more hours does she spend at
softball practice than in homeroom?

Answers

Answer:

60.0 I think

Answer:

1.25 hours or 1 hour and 15 minutes

Step-by-step explanation:

The difference in time % softball practice than in homeroom:

20% - 7.5% = 12.5%

Convert the difference into hours:

12.5*10/100 = 1.25 hours or 1 hour and 15 minutes

A diagram shows the dimensions for a local botanical garden. Measure the parallelogram to the nearest 1/4 inch. What is the area of the botanical garden diagram in square inches?

Answers

Answer:

4.8 in2

Step-by-step explanation:

2.4 x 2 =4.8

tell me if I'm wrong

Answer:

Step-by-step explanation:

After basketball practice, 8 players equally shared 3 large bottles of water. What fraction of a bottle did each player get?

Answers

It would be 3/8 since you divide the 3 bottles to 8 players

write the following comparison as a ratio reduced to lowest terms.


40 nickels to 50 dimes​

Answers

Answer:

2.5 : 2

Step-by-step explanation:

Answer:

$2 : $5

Step-by-step explanation:

40 nickels = $2

50 dimes = $5

Write down the next two terms into the given sequence :
-1; 1; 3 ;​

Answers

Answer:

5 ;7

explantion:

-1+2=1

1+2=3

3+2=5

5+2=7

the pattern is +2

ILL GIVE THE BRAINLIEST pls help me with this question EVERYTHING IS IN THE PICTURE PLS HELP DUE TODAY ​​IF YOU PUT A WRONG ANSWER ILL REPORT YOU FASTER THAN ASSIGMENT IS DUE ​​​

Answers

Answer:  the correct answer should be 160 but you said that didnt work so try 480

Step-by-step explanation:  

I just did base times Hight 8*10 which is 80*6=480

hoped this helps:))

Answer:

80

Step-by-step explanation:

V= Bh/3

Area of base= (L × W) ÷2

(8×6)÷2 = 24

Multiply by height

24×10=240

Divide by 3 (since its a pyramid therefore has 3 sides)

240/3=80

80 is your answer

184 is what percent more than 148

Answers

it is 36 percent more

Simplify 16m6-15mn+m6+17mn​

Answers

Answer:

[tex]17m^6 + 2mn[/tex]

Step-by-step explanation:

[tex]16m^6 -15mn +m^6 + 17mn[/tex]

Combine like terms, rewrite the equation and perform the operations between the coefficients,

[tex]16m^6 +m^6 -15mn+17mn[/tex]

[tex]17m^6 + 2mn[/tex]

I got the final answer :

2mn + 17m^6

a car is moving 70 miles per hour. how far does it travel in 16 seconds

Answer is what in miles

PLEASE HELP ME!!!!

Answers

Answer:

0.311 miles

Step-by-step explanation:

Convert 16 seconds to hours :

16 /60×60

= 16÷3600

= .004444hrs

Distance = Speed × time

= 70 × 0.00444444

= 0.311 miles

solve for x i’ll give brainlest to the right answer

Answers

Answer:

value of x is 11

Step-by-step explanation:

hope it helped!!!

Suppose y varies directly with x. Write an equation relating x and y. y=-12 when x=20

Answers

Answer:

[tex]y = 8 - x[/tex]

when x=20 so y=-12

a person invested $330 in an account growing at a rate allowing the money to double every 8 years. Write a function showing the amount of money in the account after tt years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year, to the nearest hundredth of a percent.

Answers

Answer:

The percentage of growth is of 9.05%.

The amount of money in the account after t years is given by [tex]P(t) = 330(1.0905)^t[/tex]

Step-by-step explanation:

Amount of money after t years:

The amount of money in an account after t years is given by:

[tex]P(t) = P(0)(1+r)^t[/tex]

In which P(0) is the initial deposit and r is the growth rate, as a decimal.

Money doubles every 8 years.

This means that [tex]P(8) = 2P(0)[/tex]. So

[tex]P(t) = P(0)(1+r)^t[/tex]

[tex]2P(0) = P(0)(1+r)^8[/tex]

[tex](1+r)^8 = 2[/tex]

[tex]\sqrt[8]{(1+r)^8} = \sqrt[8]{2}[/tex]

[tex]1 + r = 2^{\frac{1}{8}}[/tex]

[tex]1 + r = 1.0905[/tex]

[tex]r = 1.0905 - 1[/tex]

[tex]r = 0.0905[/tex]

The percentage of growth is of 0.0905 = 9.05%.

Person invested $330

This means that [tex]P(0) = 330[/tex]

So

[tex]P(t) = P(0)(1+r)^t[/tex]

[tex]P(t) = 330(1+0.0905)^t[/tex]

[tex]P(t) = 330(1.0905)^t[/tex]

The amount of money in the account after t years is given by [tex]P(t) = 330(1.0905)^t[/tex]

Kazi ran 1.2km how many centimeters did she run

Answers

9514 1404 393

Answer:

  120,000 cm

Step-by-step explanation:

There are 100 cm in 1 m, and there are 1000 m in 1 km. So, there are 100,000 cm in 1 km.

1.2 km is 120,000 cm


It cost Andrew $21 to buy 7 binders. At this price, how much would it cost him to buy 4 binders?

Answers

21/7=3 so 3$ * 4 binders would equal $12
$21/7=$3, to find the price of 1 binder
4*$3=$12, gives the price of 4

The
Olympic time for men's 400-m hurdles
has been decreasing by about 0.09 seconds per
year since 1930, when the record was 52 seconds.
Predict what the time will be in 2010

Answers

Answer:

In 2010 the time will be 44.8 seconds.

Step-by-step explanation:

Given that the Olympic time for men's 400-m hurdles has been decreasing by about 0.09 seconds per year since 1930, when the record was 52 seconds, to predict what the time will be in 2010 the following calculation must be performed:

52 - ((2010 - 1930) x 0.09) = X

52 - (80 x 0.09) = X

52 - 7.2 = X

44.8 = X

Thus, in 2010 the time will be 44.8 seconds.

50 POINTS!! WILL MARK BRAINLIEST!!! Is ΔP'Q'R' a 180° rotation about the origin of ΔPQR? Use the drop-down menus to explain your answer.

Answers

Answer:

No that would be a 90 degree

Step-by-step explanation:

The measure of angle ABC is 84, find the measure of angle ADC.

Answers

Answer:

Step-by-step explanation:

uhhh i think so its 84 is abc but adc is missing try 48  i dont know but i try

help pls what is 10,000 - 9,745 = ​

Answers

Answer:

10,000 - 9,745 = 255

Step-by-step explanation:

UwU Hope that helps

Answer: 255

→Hope this helps!←

please help will get brainliest
(the figure is not drawn to scale)
which one?
154 cm2
217 cm2
308 cm2
5488 cm2​​

Answers

308cm 2

V =14 V-6=8 - =22
K+K=14
22 x 14 =308

A normal distribution has a mean of 14 and a standard deviation of 4. What percent of values are from 14 to 22?

Answers

Answer:

80% of the values will occurs above 68.24.

Step-by-step explain

thinking this is right but im sorry if its wrong

What is the Supplimentary angle of 21°?

Answers

Answer:

159 degrees

Step-by-step explanation:

Answer:

159°

Step-by-step explanation:

We can calculate supplementary angles by subtracting the given one angle from 180 degrees. To find the other angle, use the following formula: ∠x = 180° – ∠y or ∠y = 180° – ∠x where ∠x or ∠y is the given angle.

so 180° – ∠ 21= 159°

Naomi receives a base weekly salary of $225 plus a commission of $50 for each cable service
contract she gets signed. A 6% tax is taken out of each paycheck she receives. If Naomi had
9 new clients sign contracts during her last 2-week pay period, how much money in taxes
should she expect to be taken out?

Answers

Answer:

$40.50 will be taken out in taxes.

Step-by-step explanation:

First, solve for how much Naomi will receive in a paycheck:

$225 + $50(9)

$225 + $450

$675

Now, solve for 6% tax:

$675 × 0.06

$40.50

At a high school with over 500 students, a counselor wants to estimate the mean number of hours per week that students at the school spend in community service activities. The counselor will survey 20 students in the Environmental Club at the school. The mean number of hours for the 20 students will be used to estimate the population mean. Which of the following conditions for inference have not been met?

1. The data are collected using a random sampling method.
2. The sample size is large enough to assume normality of the distribution of sample means.
3. The sample size is less than 10 percent of the population size.

Answers

Complete option:

The sample size is less than 10 percent of the population size. A. II onlyB. III onlyC. II and III onlyD. I, II, and III

Answer:

D.) I, II, and III

Step-by-step explanation:

The sample are not well randomly selected as the samples were only selected from a single source, the environmental club in the school.

Similarly only 20 samples were chosen, these 20 samples are not enough to assume normality as the minimum number of samples required to assume normality according to the Central limit theorem is 30 samples or more.

10% of the population size is :

Population size = 5000

0.10 * 5000 = 500 samples

Hence, sample size used is less than 10% of population size.

Mihai a măsurat cu pasul său latura unui lot de pământ de forma unui pătrat
şi a constatat că ea cuprinde 93 de paşi. Care este lungimea gardului care
împrejmuieşte lotul dacă Mihai, făcând 3 paşi, parcurge exact 2 m?

Answers

Răspuns:

63 metri.

Explicație pas cu pas:

Dat fiind :

Numărul de pași parcurși = 93

3 pași făcuți de Mihai = 2m

Prin urmare, 93 de pași sunt echivalenți cu:

(93 ÷ 3) * 2m

31 * 2 = 63 m

Prin urmare, lungimea laterală a parcelei pătrate = 63 m

Prin urmare, lungimea gardului care împrejmuiește lotul pătrat = 63m

What is the area of the real object that the scale drawing models?
Scale factor: 1:3
Area =
40 square cm

Answers

Answer:120 square cm

Step-by-step explanation:

40 x 3

A cooler contains 12 bottles of apple juice and 18 bottles of orange juice. You reach into the cooler without looking and pull out one bottle of apple juice. Then you reach into cooler and pull out another bottle of juice. What is the probability of pulling apple juice and then pulling another apple juice?

Answers

Answer:

P = 0.232

Step-by-step explanation:

In the cooler, we have 12 bottles of apple juice and 18 bottles of orange juice.

This adds up to a total of 30 bottles.

Now we want to find the probability of pulling a bottle of apple juice after you pulled one bottle of apple juice.

The probability of pulling a bottle of apple juice at the beginning is equal to the quotient between the number of apple juice bottles in the cooler and the total number of bottles in the cooler,

This means that 12 out of 30 are apple juice, then the probability of getting first a bottle of apple juice is:

p = 12/30

Now, we want to find the probability of getting another, we will do the same calculation than above, but now the number of bottles of apple juice is 11 (because we took one) and the total number of bottles is 29.

In this case, the probability is:

q = 11/29

The joint probability (the probability of both events happening) is equal to the product of the individual probabilities.

Then the probability of pulling apple juice and then pulling another apple juice is:

P = p*q = (12/30)*(11/29) = 0.232

If oranges are on sale for $7.27 for 5 lbs, how much would it cost you to buy 2 lbs of
oranges?

Answers

$2:91 cents that’s how much it would cost

The census is a survey of the population that gathers various details about individuals, such as age. This survey observed
that 155 out of every 200 people were 18 years old or older, Determine the probability of randomly selecting a person that
was 18 years old or older,
Express your answer as a fraction,

Answers

Answer:

31/40

Step-by-step explanation:

Just simplify the fraction

Answer:

31/40

Step-by-step explanation:

Simplify

15 cm
6 cm
The length is
meters, the width is
meters, and the area is
square meters.

Answers

Answer:

90????? There is not a lot of context. 90 is the area

Simone purchased a new car for $18,700. There
was also a 6% sales tax. What was the total
amount Simone paid for the car, including tax?

Answers

Answer:

19,822

Step-by-step explanation:

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