Ayo runs a fairground game.In each turn, a player rolls a fair dice numbered 1 - 6 and spins a fair spinner numbered 1 - 12.It costs a player £1.40 for a turn.A player can win £6 or £3 as in the diagrams:If 216 people are to play, how much profit can Ayo expect to make?

Answers

Answer 1

Using the definition of expected value, it is found that Ayo can be expected to make a profit of £55.8.

The expected value is given by the sum of each outcome multiplied by it's respective probability.

In this problem:

The player wins $6, that is, Ayo loses £6, if he rolls a 6 and spins a 1, hence the probability is [tex]\frac{1}{6} \times \frac{1}{12} = \frac{1}{72}[/tex].The player wins $3, that is, Ayo loses £3, if he rolls a 3 on at least one of the spinner or the dice, hence, considering three cases(both and either the spinner of the dice), the probability is [tex]\frac{1}{6} \times \frac{1}{12} + \frac{1}{6} \times \frac{11}{12} + \frac{5}{6} \times \frac{1}{12} = \frac{1 + 11 + 5}{72} = \frac{17}{72}[/tex]In the other cases, Ayo wins £1.40, with [tex]1 - \frac{18}{72} = \frac{54}{72}[/tex] probability.

Hence, his expected profit for a single game is:

[tex]E(X) = -6\frac{1}{72} - 3\frac{17}{72} + 1.4\frac{54}{72} = \frac{-6 - 3(17) + 54(1.4)}{72} = 0.2583[/tex]

For 216 games, the expected value is:

[tex]E = 216(0.2583) = 55.8[/tex]

Ayo can be expected to make a profit of £55.8.

To learn more about expected value, you can take a look at https://brainly.com/question/24855677


Related Questions

Find the maturity value of a loan of Php 5,000 at an interest rate of 15% in 2 years​

Answers

Answer:

  Php 6500

Step-by-step explanation:

Assuming simple interest, the value after 2 years is ...

  A = P(1 +rt) . . . . . value of loan of principal P at annual rate r for t years

  A = 5000(1 +0.15·2) = 5000(1.30) = 6500

The maturity value will be Php 6500.

Which property is shown here? (-3 + 9) + 1 = -3 + (9 + 1)

Answers

Answer:

Commutative property

Step-by-step explanation:

Answer:

Associative property I think

Step-by-step explanation:

Need help on HS geometry

Answers

Answer:

RS = 46 , RT = 38

Step-by-step explanation:

A segment joining the midpoints of 2 sides of a triangle (mid segment) is half the length of the third side, then

RS = 2 × UW = 2 × 23 = 46

RT = 2 × VW = 2 × 19 = 38

Express the perimeter of the following
rectangle in terms of n.
3n-7
n + 5
1. O 4n - 2
2. O 8n - 14
3. O 8n - 4
4. O 6n - 14

Answers

Answer:

8n - 4.

Step-by-step explanation:

Perimeter: 2B + 2L=> 2(3n - 7) + 2(n + 5)=> 6n - 14 + 2n + 10=> 8n - 4

Conclusion:

Therefore, the perimeter in terms of n is 8n - 4.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

its A

Step-by-step explanation:

8:07, 8:58, ?, 10:43, 11:37

9:51
9:50
9:53
9:49

Answers

Answer:

9:50

Step-by-step explanation:

because, 8:07 ->8:58 +51

...+52

...+53

A pattern can either follow an arithmetic sequence, a geometric sequence or a user defined sequence.

The term that completes the sequence is (d) 9:49

The sequence is given as:

8:07, 8:58, ?, 10:43, 11:37

The above sequence follows an arithmetic sequence, and the common difference (d) is calculated using:

d = 8:58 - 8:07

This gives

d = 51 seconds

The missing term (which is the third term) is then calculated using:

T3 = 8:58 + 51 seconds

This gives

T3 = 9:49

Hence, the term that completes the sequence is (d) 9:49

Read more about arithmetic sequence at:

https://brainly.com/question/6561461

Noah drove 480km in 5 hours. About how far did he drive in 2 hours?

Answers

Answer:

192km

Step-by-step explanation:

480/5 = x/2

5x = 960

/5     /5

x = 192

Answer:

If Noah's driving was at a constant rate, he drove 192 km in 2 hours

Step-by-step explanation:

In order to find the answer to this question then we can set up two equations with x meaning the km/h he is going and y as our answer.

Noah drove 480km in 5 hours can be set up as:

480 = 5x

Dividing both side by 5:

x=96

and we want to find the number of km he drove in 2 hours:

y = 2 x

because we know x=96 from the first equation

y = 196 so, therefore, Noah drove 192 km in 2 hours

in 3x + 2/3y - 15 < 0, the point (x,9) is a solution for the inequality shown. what is the possible value for x?

a: 2

b: 3

c: 4

d: 5

Answers

answer: 2

explanation:

if you plug in all of the numbers available for the equation and using 9 as a substitute for y, you'll see that it will either = 0 or be greater than 0

SOMEONE HELP!!!!!!!!!!!!!!!!!!!! I would give more points but there are people who just write random things for an answers that isnt correct just to get points.

Answers

Answer:

a)  320 is correct

b)  20 more 18 year old students

Step-by-step explanation:

a)  320 is correct

b)  20 more 18 year old students:  The only information we have in the 25 - 35 minute time frame is the data for 30 minutes:

12 years: 40 students

18 years:  60 students

Difference = 20 more 18 year old students than 12 year old students spent spent time on social media for 25 - 35 seconds.

Which inequality is graphed on the number line?

Answers

The answer is C
First you add 11 on both sides
So your left with
3a<= 18
Then divide by 3 on both sides to get
a<=6 which is plotted on the graph

Jordan goes to a high school with 1900 students. He surveyed a random sample of 240 students about their favorite sport, and 150 said that football was their favorite sport. Jordan reported to the school newspaper that football is the favorite sport of 1188 students. What inference did Jordan make? PLSS HELP QUICK !!

Answers

Answer: answer b

Step-by-step explanation:

x = 16 - 4y
3x + 4y =8
substitution method

Answers

Answer:

i think x = -4, y = 5

Step-by-step explanation:

x = 16 - 4y

3x + 4y = 8

3(16 - 4y)+4y = 8

48-12y+4y = 8

48-8y = 8

48-8 = 8y

40 = 8y

5 = y

so

x = 16 - 4y

x = 16 - 4(5)

x = 16 - 20

x = -4

MATH WILL YOU PLEASE HELP!

Answers

Answer:

I think it's -6x-18, this queston uses distributive property, so you must multiply each term inside the parenthesis to the number outside the parenthesis.

The product of b and 9 is less than or equal to 26.

Answers

9b less than or equal to 26
Divide 9 to both sides
b less than or equal to 2 and eight-ninths

HEPL!! due in 2 hours so please help or attempt! I came up with 5 different answers and don't know which one is the actual answer!!​

Answers

Answer:

Original Price = $23

Step-by-step explanation:

$5.75 is the price after a discount of 75%

Let the original price be x and x is 100% of the price

5.75 = 100%x - 75%x

5.75 = 25%x

The new price is 25% of the original because you are subtracting 75%

25% is also written as 0.25

5.75 = 0.25x

x = 5.75/0.25

x = 23

The original price is 23

-Chetan K

Find the value of theta, to the nearest hundredth if cos they have is -0.7 and theta is in quadrant 2

Answers

Step-by-step explanation:

if I understand you correctly, then

cos(theta) = -0.7

then Theta = 134.427004...°

and that is rounded 134.43°

Pls solve this with solution​

Answers

Okay so for these problems it’s best to break up the problem and solve it step by step. First, 10 to the 5th power(the little 5) is the same as 10x10x10x10x10=100,000. So, 10 to the second power(little 2 on top) is equal to 10x10=100. Then after you find your answer there the problem becomes easier and all that’s left is to multiply and add. Next multiply 6x100,000=600,000 and 6x100=600. Finally we add them, 600,000 + 600= 600,600. 600,060 does not equal 600,600 so the equation is false.

A survey of 500 college students moving into their dorm revealed that 425 brought a microwave, 380 brought a video game console, and 50 brought neither a microwave nor game console. A survey participant is randomly selected. Let M be the event the participant brought a microwave and let C be the event the participant brought a video game console. Organize these events in a two-way table. What is the probability that the participant did not bring a microwave or did not bring a console, P(MC or CC)?

0.10
0.29
0.39
0.90

Answers

Answer:

0.90

Step-by-step explanation:

I’m doing the unit test

Answer:

0.29

Step-by-step explanation:

The probability that they brought both is .90

The probability of neither is .29, which is what this question is asking

How many different terms are in the expression? 28s + 3t+ 6b + 21f

Answers

Answer:

4

Step-by-step explanation:

In math, the word difference is the result of subtracting one number from another. It refers to the difference in quantity between two numbers. In math, we get the difference between two numbers by subtracting the subtrahend (the number being subtracted) from the minuend (the number being subtracted from).

Hi, I have a question it is kinda hard but I think i got it, if it's wrong plz tell mee

Solve for X

5-x+6=4

X=3

Answers

5-x + 6 = 4

Combine like terms:

11-x = 4

Subtract 11 from both sides

-x = -7

Divide both sides by -1

X = 7

Answer: x = 7

Question:-

Solve for X

5-x+6=4

Answer:-

x = 7

Explanation:-

=> 5-x + 6 = 4

=> (5+6)-x = 4

=> 11-x = 4

(subtract both the sides by 11)

=> -x = -7

(divide both the sides by -1)

=> x = 7

make t the subject q= 1+3t/2-t

Answers

Answer:

t = dfrac-1 + 2 q3 + q.

Step-by-step explanation:

What is the gradient of the graph shown?

Give your answer in its simplest form.

Answers

Answer:

2

Step-by-step explanation:

Choose 2 points on the graph: (0, -2) and (1, 0)

[tex]\boxed{ gradient = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]

Gradient of graph

[tex] = \frac{0 - ( - 2)}{ 1 - 0} [/tex]

[tex] = \frac{0 + 2}{1} [/tex]

= 2

Answer:hope it helps!

Step-by-step explanation:

cannot be bothered

The blueprint for Moreno​'s living room has a scale of 2 inches equals 3 feet. The family wants to use a scale of 1 inch equals 2 feet. What is the width of the living room on the new​ blueprint? (The width is 8)

Answers

If the 8 you’re talking about is in inches then it would be 16 feet but if it’s 8 feet then it’s 4 inches

Four people can paint a fence in 6 hours how long would three people take to paint it?

Answers

Answer:

8 hours

Step-by-step explanation:

4 people = 6 hours

→ Work out how long 1 person takes

1 person = 24 hours

→ Work out how long 3 people takes

3 people = 8 hours

Choose the true statements.
O
A linear function is expressed by a graph of a line that
crosses both axes at the origin. An equation is written in
slope-intercept form to express the same function as
shown in the graph. From just this information, what
statements can be made?
The slope of the equation must be positive.
The y-intercept of the equation is zero.
It is possible that the line on the graph is horizontal.
The slope of the equation must be negative.

Answers

Answer:

The y-intercept must be zero.

It is possible that the line is horizontal.

Step-by-step explanation:

The description states that the line "crosses both axes at the origin."  That would mean that the point (0,0) is on the graph.  The y-intercept is the value of y when x=0.  We see that it is zero in this case (0,0).  

The description says nothing about the slope.  So it could be either positive or negative.  But it could also mean that the slope is zero.  A zero slope would be a horizontal line.  So that is a second statement that is true:  "It is possible that the line on the graph is horizontal."

Answer:

its b and c

Step-by-step explanation:

Zoe charges £9 per student to attend a dance class. There are y students in the class.

a . Write an expression for the total amount she charges for a class.

b. How much does she charge for 5 students?

c. How many students must she have in the class to make £72?

Answers

a. 9y ( 9 x y)

b. 9(5) - She charges 45$ for 5 students

c. 9y= 72
y = 72/9
y = 8

She must have 8 students in her class.

Help Plssss it is due tommorrow!!!!! I think it is A i am not sure help

Answers

Answer: congruent bases

Step-by-step explanation:

what makes a trapezoid a trapezoid is that the bases are different! the side on top and bottom are different.

congruent base :) hope this helped

Solve
x ^ 4 -8x ^ 2 – 9 = 0

Answers

Answer: 0 is the answer

Step-by-step explanation: your welcome its 0

Combine the like terms to create an equivalent expression.
\large 9p+3p

Answers

Step-by-step explanation:

there is not much here.

all I can see is

9p + 3p

and that is 12p (as 9+3 = 12)

Which expression shows a way to factor 20+24?

Answers

Answer:

20+24= 2(10+12) = 4(5+6)

Those are two ways to factor 20+24.

A shop has a sale that offers 20% off all prices.On the final day reduce all the sale prices by 25%.Linz buys a radio on the final day.Work out the overall percentage reduction on the price of the radio

Answers

Answer:

40%

Step-by-step explanation:

Original price = x

Sale = 20% off

20% / 100 = 0.2 to convert from a percent to a decimal

Sale = x - 20% of x = x - 0.2x = 0.8x

Sale price = y = 0.8x

Reduction of sale prices = 25% = 0.25

Reduction = y - 25% of y = y - 0.25y = 0.75y

End price in terms of original price (x):

0.75y = 0.75(0.8)x

          = 0.6x

End price = 0.6 or 60% of original price, coming out to a 100-60 = 40% overall percentage reduction

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