Suppose that two teams play a series of games that end when one of them has won i games. Suppose that each game played is, independently, won by team A with probability p. Find the expected number of games that are played when i = 2. Also show that this number is maximized when p= 21.

Answers

Answer 1

Answer:

a) E(x) = -2p^2 + 2p + 2

b) Number is maximized when p = 1/2

Step-by-step explanation:

Determine the Expected number of games  when ( i ) = 2

The number of possible combinations that both teams win two games :

AA, BB, ABB, ABA, BAA, BAB  = 6 combinations

P( team A winning ) = p

P( team B wins ) = 1 - p

Attached below is the detailed solution on the expected number of games

expected number of games ; E(x) = -2p^2 + 2p + 2

ii) Number is maximized when p = 1/2

Suppose That Two Teams Play A Series Of Games That End When One Of Them Has Won I Games. Suppose That
Answer 2

In this exercise we will use the knowledge of probability and combination, so we have what will be:

a)[tex]E(x) = -2p^2 + 2p + 2[/tex]

b)[tex]p = 1/2[/tex]

Organizing the information given in the statement as:

Expected number of games  when ( i ) = 2

A)The number of possible combinations that both teams win two games :

[tex]AA, BB, ABB, ABA, BAA, BAB = 6 \ combinations\\P( team\ A \ winning ) = p\\P( team \ B \ wins ) = 1 - p\\E(x) = -2p^2 + 2p + 2[/tex]

B) To calculate the maximum number we must solve the quadratic equation, like this:

[tex]p=1/2[/tex]

See more about probability at brainly.com/question/795909


Related Questions

a recent survey shows that 66% of college students have a cat and 37% have a HBO subscription. Assuming these two events are independent, what is the probability that a randomly selected student has neither a cat nor HBO

Answers

Answer:

[tex]P(C'\ and\ H') =0. 2178[/tex]

Step-by-step explanation:

Let

[tex]C \to[/tex] Student with cat

[tex]H \to[/tex] Student has HBO sub

[tex]P(C) = 66\% \\ P(H) = 37\%[/tex]

Required

[tex]P(C'\ and\ H')[/tex]

This is calculated as:

[tex]P(C'\ and\ H') = P(C') * P(H')[/tex]

Using complement rules, we have:

[tex]P(C'\ and\ H') = [1 - P(C)] * [1 - P(H)][/tex]

So, we have:

[tex]P(C'\ and\ H') = [1 - 66\%] * [1 - 37\%][/tex]

[tex]P(C'\ and\ H') = [33\%] * [66\%][/tex]

[tex]P(C'\ and\ H') =0. 2178[/tex]

Estimate the product of 0.235 and 13.467 to the nearest hundredth. Round each value to the nearest hundredth before multiplying. Your final answer should also be rounded to the nearest hundredth.

Answers

Answer:

0.235 = 0.24

13.467 = 13.47

0.24+13.47=13.71

Complete the statement below. A Type II Error is made... Choose the correct answer below. A. A Type II Error is made when​ there's not enough evidence to reject the null hypothesis and the null hypothesis is true. B. A Type II Error is made when​ there's evidence to reject the null​ hypothesis, but the null hypothesis is true. C. A Type II Error is made when​ there's not enough evidence to reject the null​ hypothesis, but the null hypothesis is not true. D. A Type II Error is made anytime we do not reject the null hypothesis.

Answers

I think it’s d I believe

What are the divisible number(s) for 430?

Answers

Answer:

The numbers that 430 is divisible by are 1, 2, 5, 10, 43, 86, 215, and 430.

This is how you do it

in alska the colderst temprauter ever recorded is -80 that is much colder than in hawil where the coldest temperature is 15

Answers

Answer: What are we supposed to do ???

find the missing length indicated​

Answers

Answer:

192

Step-by-step explanation:

geometric mean theorem :

with p and q being the segments of the Hypotenuse, then

h = x = sqrt(p×q)

p = 144

q = 400-144 = 256

h = x = sqrt(144×256) = 12×16 = 192

A medical researcher is using rats to do an experimental test to determine the appropriate dosage for a new cancer drug. Each rat will be given a different dosage of the drug. The oncologist will then measure the growth rate of the cancerous tumor. What best describes the input and output variables that will be used in this experiment?

Answers

The input of the experiment is the amount of dose of the drug and the output is the growth rate of the cancerous tumor.

Given information:

A medical researcher is using rats to do an experimental test to determine the appropriate dosage for a new cancer drug.

Each rat will be given a different dosage of the drug.

The oncologist will then measure the growth rate of the cancerous tumor.

Now, in the experiment, the oncologist tries to study or calculate the growth rate of a cancerous tumor. So, the output that he/she will get will be the growth rate of the cancerous tumor.

The experiment is done on the rate by giving them a dosage of the drug. The dosage can vary based on the study criterion. So, the amount of dosage of the drug should be the input of the experiment.

Therefore, the input of the experiment is the amount of dose of the drug and the output is the growth rate of the cancerous tumor.

For more details, refer to the link:

https://brainly.com/question/5527886

A particle is moving such that its height h at time t is given by h(t) = 2 + 8t - 3t^2 + 1/5t^3. The average velocity of the particle on the period [0,3] is

Answers

t=3

[tex]\\ \Large\sf\longmapsto h(t)[/tex]

[tex]\\ \Large\sf\longmapsto 2+8t-3t^2+\dfrac{1}{5}t^3[/tex]

[tex]\\ \Large\sf\longmapsto 2+8(3)-3(3)^2+\dfrac{1}{5}(3)^3[/tex]

[tex]\\ \Large\sf\longmapsto 2+24-3(9)+\dfrac{27}{5}[/tex]

[tex]\\ \Large\sf\longmapsto 26-27+5.4[/tex]

[tex]\\ \Large\sf\longmapsto -2+5.4[/tex]

[tex]\\ \Large\sf\longmapsto h(t)=3.4m[/tex]

You are enrolling swimmers in a study on lung capacity. You want 25% of your sample to be those who compete at 100m or less distances and 50% to be swimmers who compete at 100m-500m distances and 25% to be swimmers who compete at >500m distances. You begin enrolling for your study at 5am at the pool. By 9 AM you have all of your 100-500m swimmers enrolled, and all of your >500m swimmers enrolled. This is an example of what type of sampling method

Answers

Answer:

Stratified sampling

Step-by-step explanation:

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

In this question:

People divided by groups, for each group(<100, >100<500, >500), a number(not all) is selected, so stratified sampling.

Convert 2546 in base 10 to base 5

Answers

Answer:

40141

Step-by-step explanation:

(d) (8x2 + 7y2 – z2 + 2yz + 3xz – 5xy) * (2x – 3y) vertical method

Answers

Answer:

(8x²+7y²–z²+2yz+3xz–5xy) × ( 2x–3y)

= (16x³+14xy²–2z²x+4yzx+6x²z–10x²y –24yx²–21y³+3z²y–6y²z–9xzy+15xy²)

=( 16x³+29xy²–2z²x–5xyz+6x²z–34x²y–21y³+3z²y–6y²z)

[tex] = 16 {x}^{3} - 21 {y}^{3} - 2 {z}^{2}x + 3 {z}^{2} y - 5xyz - 6 {y}^{2} z + 6 {x}^{2} z - 34 {x}^{2} y+ 29x {y}^{2} [/tex]

I hope I helped you^_^

6x — Зу = 5
y - 2x = 8
How many solutions does the system have?

Answers

9514 1404 393

Answer:

  none

Step-by-step explanation:

Multiplying the second equation by -3 gives ...

  6x -3y = -24

Values of x and y that satisfy this equation cannot also satisfy the first equation ...

  6x -3y = 5

There are no solutions to this system of equations.

__

The equations describe parallel lines. There is no point of intersection.

The fuel efficiency of a vehicle is 28 miles per gallon and gasoline cost 2.25 per gallon. What is the cost per mile to drive the vehicle?​

Answers

Answer:

$.08 per mile

Step-by-step explanation:

$2.25          gallon

------------ * ---------------

gallon          28 miles

$2.25

-------------

28 miles

$.080357143 per mile

Rounding to the nearest cent

$.08 per mile

There are 5 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible?

Answers

Answer:

60

Step-by-step explanation:

To begin, we can look at combinations and permutations. A permutation or combination is when we need to find how many possibilities there are to choose a certain amount of objects (in this case, candidates) given an array of options (members on the board)

Combinations are when the order doesn't matter, and permutations are when the order does matter. Here, we know that we care whether someone is chairperson or secretary. If we were to just choose three for an "elite" board, and there were no specific positions in the board, then order would not matter. However, because it does matter which person gets which role, order does matter.

Assuming that someone cannot have more than one role, we know that this is a permutation without repetition. The formula for this is

(n!) / (n-r)!, where we have to choose from n number of people and choose r number of people. We have 5 members to choose from, and 3 people to choose, making our equation

(5!) / (5-3)! = 120 / 2! = 120/2 = 60

The final price of the textbook for an English literature course is 13.5% more than the listed price when tax and shipping costs are included. If the listed price is $147, what is the final price of the textbook?

(Round to the nearest dollar.)

Answers

Answer:

The final price of the textbook rounded to the nearest dollar is $167

Step-by-step explanation:

To solve this problem, we need to find out what 13.5% of $147 equals.

13.5% = 0.135

0.135 x $147 = $19.845

$147 + 19.845 = 166.845

Round to the nearest dollar to get $167

If x + 1 =3, then x=

Answers

Answer:

x = 2

Step-by-step explanation:

x + 1 = 3

transpose

x = 3-1

x= 2

What is the value of the expression below? (27^2/3)^1/2
A. 9
B. 81
C. 27
D. 3​

Answers

I think it might be A

Answer:it’s 3

Step-by-step explanation:

Source trust me bro

How to divide using area model

Answers

Answer:

In mathematics, an area model is a rectangular diagram or model used for multiplication and division problems, in which the or the and define the length and width of the rectangle.

We can break one large of the rectangle into several smaller boxes, using number bonds, to make the calculation easier. Then we add to get the area of the whole, which is the or quotient.

To multiply two 2-digit numbers, using the area model, follow the given steps:

Write the multiplicands in expanded form as tens and ones.

For example, 27 as 20 and 7, and 35 as 30 and 5.

Draw a 2 × 2 grid, that is, a box with 2 rows and 2 columns.

Write the terms of one of the multiplicands on the top of the grid (box). One on the top of each cell.

On the left of the grid, write the terms of the other multiplicand. One on the side of each cell.

Write the product of the number on the tens in the first cell. Then write the product of the tens and ones in the second and third cell. Write the product of the ones in the fourth cell.

write the product in the cell

Finally, add all the partial products to get the final product.

Here, for example, the area model has been used to multiply 27 and 35.

area model multiplication

Let us see how to find the product of 3-digit number by a 2-digit number using the area model.

Find the Product using Area Model

Let us now use the area model for the division. Here, we divide 825 by 5.

Area Model Division 1

Area Model Division 2

Fun Facts

The area model is also known as the box model.

The area model of solving multiplication and division problems is derived from the concept of finding the area of a rectangle. Area of a rectangle = Length × Width.

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PLEASE HELP LOOK AT PICTURE

Answers

the answer is option 2. try subbing in the values of each of the X values and you’ll discover that option 2 is correct since the answers match with the Y values

Domain and range of g(x)= 5x-3/2x+1
Solve for domain and range?

Answers

The domain and the range

A $22,000 loan was taken out. If $24,805 is due at the end of the loan after being compounded daily at 2.5%, how many
years was the loan for? (Round to the nearest tenth of a year)
Provide your answer below

Answers

9514 1404 393

Answer:

  4.8 years

Step-by-step explanation:

Solving the compound interest formula for the number of years gives ...

  t = log(A/P)/(n·log(1 +r/n))

where principal P invested at rate r compounded n times per year produces value A after t years.

  t = log(24805/22000)/(365·log(1 +0.025/365)) ≈ 4.800

The loan was for 4.8 years.

7. Find HCF of: x'y and ly*
8. Find LCM of 4x - 20 and 6x - 30
9. Factorize Factorize: -m-+ 1 + me
10. Factorize: 4x100
11. Simplify: V18+ va 12. If a = 2, b = 3 and c= 4, fmd the value of a b c 13. Subtract: 125- 45 a--200+ 14. Simplify: ***​

PLEASE HELP ME

Answers

Answer:

7 ans-HCF is y

Step-by-step explanation:

soln

first expression=X and y

second expression=l and y

so HCF means common so the Ans is y

urgent !!!! HELP NEEDED

Answers

Answer:

[tex]352\ yd^2[/tex]

Step-by-step explanation:

1. Approach

The surface area of a three-dimensional figure is the two-dimensional space around the figure. Simply put, if one was going to wrap the figure up in paper, the surface area is the amount of paper one would need to wrap the entirety of the figure. One can find the surface area of a figure by finding the area of each individual facet of the figure and then adding up the areas.

2. Finding the area of the triangular faces

The formula to find the area of a triangle is the following:

[tex]A_t=\frac{b*h}{2}[/tex]

Where (b) is the base of the figure, and (h) is the figure's height. Since there is only one type of triangular face, one only has to find the area of one triangular face and then multiply its measurement by four.

Triangle 1

[tex]A_t=\frac{b*h}{2}[/tex]

[tex]A_t=\frac{11*10.5}{2}[/tex]

[tex]A_1=\frac{115.5}{2}[/tex]

[tex]A_t=57.75[/tex]

3. Finding the area of the quadrilateral

The following formula can be used to find the area of a quadrilateral:

[tex]A_q=b*h[/tex]

Substitute the dimensions of the quadrilateral in and solve for its area:

[tex]A_q=b*h[/tex]

[tex]A_q=11*11[/tex]

[tex]A_q=121[/tex]

4. Find the total surface area of the figure

To find the total surface area of the figure, add up all of the area values of its faces. Remember the area of the triangular face is multiplied by four because there are four triangular faces.

[tex]4(A_t)+(A_q)=A[/tex]

[tex]4(57.75)+121=A[/tex]

[tex]231+121=A[/tex]

[tex]352=A[/tex]

the cost of 1 kg tomato is RS . 75.Find the cost of 14 kg​

Answers

Answer:

Cost of 1kg tomato=rs.75

Cost of 14kg tomato=(75×14)

rs.1050

Help on 3,5,7,9,11,13.15,17, please thank you

Answers

Answer:

3. 6a+60

5. 25+5w

7. 90-10t

11. 4.5-12c

13. f-2

15. 12z+1.5

Step-by-step explanation:

3.

6(a+10)

Multiply 6 by both factors in the parentheses, in this case, a and 10.

6*a = 6a

6*10 = 60

6(a+10) = 6a + 60

I only put the step- by- step explanation for #3, but you should be able to figure the rest out with that.

The principle

P=6000 A=6810 T=3 years

Answers

Answer:

incomplete question

Step-by-step explanation:

that is what is wrong with your question

Answer:

r = 4.3%

Step-by-step explanation:

6810= 6000(x)^3

6810/6000=  (x)^3

x = 1.043114431

r = 043114431

What is the probability of throwing a total score of 10 or less with two dice?​

Answers

hope it helps

please mark Brainliest

13.
а/8 = $1.25
Can someone help explain

Answers

Answer:

a= $10.00

Step-by-step explanation:

It's very simple. Move /8 to the other side of the equation. It should give you $1.25 x 8. Solve the multiplication and you should get $10.00.

If I didn't make my explanation clear enough, please comment. I sometimes don't even explain myself very well.

Answer:

a = 10

Step-by-step explanation:

a/8 = 1.25

multiply both sides by 8 to isolate a.

(8)(a/8) = 1.25(8)

which gives you

a = 1.25(8)

which simplifies to

a = 10

Write a quadratic equation with integer coefficients having the given numbers as solutions.

Answers

9514 1404 393

Answer:

  x² -22 = 0

Step-by-step explanation:

The roots are opposites, so the equation is pretty simple.

  x = ±√22

  x² = 22 . . . . . square both sides

  x² -22 = 0 . . . . your quadratic equation in standard form

Which choices are equivalent to the quotient below? Check All That Apply.

Answers

Answer:

Option C. √5/3

Step-by-step explanation:

We'll begin by simplifying √15 / 3√3. This can be obtained as follow:

√15 / 3√3

Rationalise

√15 / 3√3 × (√3 /√3)

(√15 × √3) / (3√3 × √3)

√45 / (3 × 3)

√45 / 9

Recall:

√45 = √(9 × 5) = √9 × √5 = 3√5

Thus,

√45 / 9 = 3√5 / 9

√45 / 9 = √5 / 3

Therefore,

√15 / 3√3 = √5 / 3

Thus, option C gives the right answer to the question.

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