In a game, 2 players each flip a coin. I fboth land on heads, player A gets 2 points and player Bioses 1 points. Ifboth land on tails, player B gets 2 points and player A loses 1 point. Find the expected value of the game for each player.

Answers

Answer 1

Building a probability distribution, it is found that the expected value for both players is of 0.25 points.

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

In this problem, the four possible outcomes, considering Player A - Player B, are:

H - H

T - H

H - T

T - T

That is, considering a success as the number of heads, the distribution is:

[tex]P(X = 0) = 0.25[/tex]

[tex]P(X = 1) = 0.5[/tex]

[tex]P(X = 2) = 0.25[/tex]

For Player A, the earnings of each outcome are: -1, 0 and 2

Hence, the expected value is:

[tex]E_A(x) = -1(0.25) + 0(0.5) + 2(0.25) = 0.25[/tex]

For Player B, the earning of each outcome are: 2, 0 and -1.

Hence:

[tex]E_B(x) = 2(0.25) + 0(0.5) - 1(0.25) = 0.25[/tex]

The expected value for both players is of 0.25 points.

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Related Questions

The sum lf two numbers is 10. The difference between the two numbers is 4: what is the smaller numerical?

Answers

Answer:

3

Step-by-step explanation:

The two numbers are 3 and 7, and 3 is the smaller one

Step-by-step explanation:

x, y are the 2 numbers.

x + y = 10

y - x = 4

that gives us

y = x + 4

and we use that in the first equation :

x + x + 4 = 10

2x = 6

x = 3

y = x + 4 = 3 + 4 = 7

so, yes, the smaller number is 3.

Ima just say the question to: "The length of each of the two congruent sides of an isosceles triangle is 2x + 3. The length of the third side is 2x. Its perimeter is 36 centimeters. Write and equation that could be used to find the value of x. Solve for x and then find the length of all three sides." 100 points!!!!

Answers

Answer:

x = 5

Congruent sides = 13 cm each

3rd side = 2(5) = 10 cm

Step-by-step explanation:

2(2x+3)+2x = 36

4x+6+2x = 36

6x = 36-6

x = 30/6

x = 5

Congruent sides = 2(5)+3 = 13

Line y=2x+3 is tangent to a circle with center (2,-3). Which of the length of the radius of the circle?​

Answers

Answer:

[tex]2\sqrt{5}[/tex]

Step-by-step explanation:

Since it is tangent to the center, the perpendicular line passes through the center, (2,-3). We find the slope of the perpendicular line to be -1/2 (perpendicular to a slope of 2). We can use point slope form to find the line from the tangent line to the center:

y+3=-1/2(x-2)

We can simplify this to

y= -1/2x-2

We can then check the point of intersection:

-1/2x-2=2x+3

-5=2.5x

x=-2

we can plug this in to the first equation to get y=2(-2)+3=-1

So the point of intersection of the circle and the tangent line is (-2,-1)

Then we find the distance of this point to (2,-3) and we can use pythagorean theorem.

[tex]\sqrt{(-2-2)^{2}+(-1-(-3))^{2} } =\sqrt{(-4)^{2}+2^{2} } =\sqrt{20} =2\sqrt{5}[/tex]

The radius of the circle is [tex]2\sqrt{5}[/tex]

For Line y=2x+3 is tangent to a circle with center (2,-3) then the length of the radius of the circle is 10/√5

What is Distance?

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

The line y=2x+3 is tangent to the circle with center (2,-3)

The distance from the center of the circle to the line is equal to the radius of the circle.

The distance from a point (x₁, y₁) to a line Ax + By + C = 0 is given by the formula:

d = |Ax₁+ By₁ + C| /√A² + B²

The equation of the line is y = 2x + 3, which can be written in the form Ax + By + C = 0 as (-2)x + y - 3 = 0.

d = |-2(2) + (-3) - 3| / √(-2)² + 1²

d=10/√5

The radius of the circle is equal to the distance from the center to the tangent line, which is:

radius = 10/√5

Hence, for Line y=2x+3 is tangent to a circle with center (2,-3) then the length of the radius of the circle is 10/√5

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A student has a savings account with $475 in it.
She deposits $125 of her paycheck into the account
every week. Her goal is to save $7,000 for college.
How long will it be before she has $1350?

Answers

Answer: 7 weeks

Step-by-step explanation:

Let x represent number of weeks

Let y represent the total amount

Amount = Paycheck deposited * number of weeks + Initial amount

y = 125x + 475

Number of weeks until she has $1350

1350 = 125x + 475

125x+475-475=1350-475

125x=875

x=7

Therefore, the student will have $1350 in her bank account after 7 weeks

Answer 7 Weeks
I Hope This Helps

Find the unit price for a 9 oz bottle of ketchup for 88cents. round answers to the nearest tenth of a cent. ________ cents per ounce

Answers

Answer:

0.1 cents per ounce

Step-by-step explanation:

You know that you paid 88 cents for the whole bottle of ketchup and the whole body contains 9oz of ketchup. Every one ounce is equal to 9.8 cents. You simply need to divide the total amount of the item by the weight (9 ounces) to get 0.09 or 0.1 when rounded.

[tex]\frac{88 cents}{9oz}=0.1 cents per ounce[/tex]

What is the missing addend what +10=235

Answers

The missing number is 225

225+10=235

PLS ANSWER 30 POINTSSS

Answers

Answer:

letter B po

Step-by-step explanation:

basta letter B may ganyan din kame eh

given the function below, which of the following values will result in f(x)=10

f(x)=1/2x+8​

Answers

Answer: x=4

Step-by-step explanation:

1/2x+8=10

Subtract 8 from 10

Multiply 2 to 2

x=4

Step-by-step explanation:

1/2(10)+8=

1/20+8=

161/20=

8.05

a husband and wife discover that there is a 4% probability of their passing on a hereditary disease to 3 of their children if they plan to have their children what is the probability of the event that at least one child will inherit the disease

Answers

"4% probability of their passing on a hereditary disease to 3 of their children"

I'm not sure if this means that the possibility of them passing the disease to one child is 4%, or if the probability of them passing the disease to the collective three children is 4%.

In case its the first one:

To make this a little easier, if you think about it the only possible way for the condition "at least one child will inherit the disease" to be untrue is if all 3 children do not have the disease. Therefore we just need to calculate the probability of all 3 children not having the disease.

if the chance of having the disease is 0.04, then the chance of not having it is 0.96

for three children: 0.96*0.96*0.96

=  0.884736

to find the chance of this not happening:

1 - 0.884736

= 0.115264 ≈ 12%

there is a 12 percent chance at least one of the children will inherit the disease

In case its the second one:

the probability of all 3 children having the disease is 0.04,

the probability of 1 child getting the disease is unknown, x.

this means

x*x*x = 0.04

x ≈ 0.342

now we just basically repeat the steps above

1 - 0.342

= 0.658 (probability that one child does not get the disease)

0.658 * 0.658 * 0.658

= 0.284890312 (probability that all 3 children do not get the disease)

1 - 0.284890312

= 0.715109688 ≈ 72%

there is a 72 percent chance at least one of the children will inherit the disease

Can someone help me please

Answers

Answer: 56 times

Pls mark brainleist i really need it

HELP ASAP! QUICK ALGEBRA 20 POINTS!!!!!!! WILL AWARD BRAINLIEST

Answers

Answer:

On the first image: if 45 divides the number, it means you can rewrite it as 45 times something. Let's play with powers of 9 to see if you can make a 45 or rewrite it as a product of a power of 9 and a power of 5.

On the second and third images, it's just a matter of collecting common factors. I collected the minus sign so the parenthesis starts with a positive term, but it's a matter of personal preference.

20.4 is what percent of 17?

Answers

Answer:

120%

20.4 is 120% of 17.

Step-by-step explanation:

20.4/17 = 1.2

1.2 x 100 = 120%

Hope this helped. Have a good one!


460,451,442,...
Find the 37th term.
Find the 37th term.

Answers

Answer:

The 37th term is 136.

Step-by-step explanation:

The sequence has a common difference therefore, it is an arithmetic sequence

The formula for arithmetic sequence is

[tex]an = a1 + (n - 1)d[/tex]

where,

an is the nth term,

a1 is the first term,

n is the term number and

d is the common difference

Find the 37th term.

an = a1 + ( n-1 ) d

a37 = 460 + ( 37-1 ) -9

a37 = 460 + ( -324 )

a37 = 136

Solve for X : 3/8 = 27/x

Answers

Answer:

x = 72

Step-by-step explanation:

3/8=27/x

cross multiply

3*x=3x   27*8=216

divide

216/3=x

x=72

3) A Jewelry artist charges $7.00 for each pair of earrings she sells. in 3 hours, she sells 15 pairs of
earrings. At that rate, how much money could she earn from selling earrings for 5 hours?

Answers

Answer: $175

Step-by-step explanation:

$7.00 x 15 = $105.00

$105.00 / 3 hours = $35/hr.

$35 x 5 = $175

If a number has 8 as a factor, then both 2 and 4 are factors

Answers

yes that is correct

James joins Club One which charges a monthly membership of $19.99. In 6 months, will he spend less than $120 in all?

Answers

Answer:

120

Step-by-step explanation:

round 19.99 to 20 and do 20 times 6

Juana is making a triangular hat for a puppet. If two of the three angles of the hat both measure 30°
, what is the measure of the third angle?

Enter the correct answer in the box.

Answers

30+30=60 180-60=120

So the answer is 120

W(x)=3x^2-3x .find w(5+t)

Answers

Answer:

[tex]60+27t+3t^2[/tex]

Step-by-step explanation:

Let's put 5+t wherever we have x in the original: rest is simple algebra.

[tex]w(5+t) = 3(5+t)^2 -3(5+t) = 3(25+10t+t^2)-15-3t =75+30t+3t^2-15-3t =60+27t+3t^2[/tex]

Consider the following function. f(x)= 4x+7 Place the steps for finding f -1(x) in the correct order.

Answers

Answer:

To find an inverse, you need to replace f(x) with y. Then switch the x and y's in your equation and solve for y.  This will find f^-1(x).

Step-by-step explanation:

Find the slope and the y-intercept of the line with the equation 8y - x + 7 = 0.

Answers

8y - x + 7 = 0 => y = 1/8x - 7/8
The slope is: 1/8
Ok done. Thank to me :>

Graph the function g(x) = 2x2 + 8x - 1

Answers

Answer:

(-2,-9)

(0,-1)

Step-by-step explanation:

I solved in desmos.

HELP


HOW AM I MEANT TO ANSWER THIS QUESTION I WOULD ASO LIKE ANSWER.


THX

Answers

Answer:

= 108

Step-by-step explanation:

the rectangle = 12 * 5 = 60

plan A:

the triangle A with H = (13 - 5)/2 = 8/2 = 4

then triangle A = [tex]\frac{1}{2}[/tex] * 6 * 4 = 24/2 = 12

total triangles = 12 * 4 = 48

hexagon area = 60 + 48 = 108

plan B:

there 13 - 5 = 8

because there are identical triangles, so we can shape both of it being a rectangle with short line is 8/2 =4, and long line is 12

then we calculate that rectangle area = 12 * 4 = 48, then total of the hexagon = 60 + 48 = 108

Jill and Tim have the same number of toy cars. Tim has 10 red cars and 20 blue cars. Jill has 8 red cars, 15 blue cars, and some yellow cars. How many yellow cars does Jill have?​

Answers

Answer:

7 yellow cars

Step-by-step explanation:

Tim has 30 cars, so Jill has 30 as well. She has 8+15=23 red and blue cars. This means that there are 7 yellow cars.

Simplify the expression.
5(2 +t) – 3(t + 1)
please help as soon as possible

Answers

Answer:

7 + 2t is the simplest form of your equation.

Hope this helps! :D

what is
The lines shown below are parallel. If the green line has a slope of -3/7
the slope of the red line?

Answers

if the lines were parallel they would have the same slope. if the lines were perpendicular then the slope would be the negative reciprocal slope. The answer to your question would be -3/7.

(64/8/ 4 + 7 – 2) • 5 =

Answers

Answer:

35

Step-by-step explanation:

Let me know if I got it right

Solve for the value of X

Answers

Check the picture below.

I believe that the answer is 10.
X=10

How much larger is 8 x 10^8 compared to 2 x 10^5?
О 4 times larger
O 40 times larger
O 400 times larger
O 4,000 times larger

Answers

8 x 10^8 is 4,000 larger than 2 x 10^5
the answer is D,
8x10^8 = 800000000
2x10^5= 200000
so it’s 4,000 times larger

Given the equation y=|x| complete the table of values

Answers

Answer:

2,1,0,1,2

Step-by-step explanation:

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