Arthur has a box which contains 6 black balls and n (n ≥ 2) white balls, then at random, he takes 3 balls from the box. If the probability of taking any ball is the same and Pₙ is the probability of taking 1 black ball and 2 white balls, what is the largest possible value for Pₙ?​

Answers

Answer 1

Answer:

11/68 or 0.1618

Step-by-step explanation:

Balls

Black - 6White - n

Options of getting 3 balls

1. White, black, black2. Black, white, black3. Black, black, white

Probability P(n) in each option

1. WBB

P(w) = 6/(n + 6)P(b1) = n/(n + 6 - 1) = n/(n + 5)P(b2) = (n - 1)/(n + 5 - 1) = (n - 1)/(n + 1)

P(n) =

P(w)P(b1)(P(b2) = 6/(n+6) × n/(n + 5) × (n - 1)/(n + 4) =6n(n - 1)/(n + 6)(n + 5)(n + 4)

2. BWB

P(b1) = n/(n + 6)P(w) = 6/(n + 6 - 1) = 6/(n + 5)P(b2) = (n - 1)/(n + 5 - 1) = (n - 1)/(n + 4)

P(n) =

P(b1)P(w)(P(b2) = n/(n+6) × 6/(n + 5) × (n - 1)/(n + 4) =6n(n - 1)/(n + 6)(n + 5)(n + 4)

3. BBW

P(b1) = n/(n + 6)P(b2) = (n - 1)/(n + 6 - 1) = (n - 1)/(n + 5)P(w) = 6/(n + 5 - 1) = 6/(n + 4)

P(n) =

P(b1)P(b2)(P(w) = n/(n+6) × (n - 1)/(n + 5) × 6/(n + 4) =6n(n - 1)/(n + 6)(n + 5)(n + 4)

Final equation is same for each case:

P(n) = 6n(n - 1) / (n + 6)(n + 5)(n + 4)

The easy way to find the maximum is to try the numbers or graph.

Both of the methods give the maximum integer n = 11 or n = 12

See attached graph

At both values n we get P(n):

P(11) = 6*11*10 / 15*16*17 = 11/68 = 0.1618 (rounded)P(12) = 6*12*11 / 16*17*18 = 11/68 = 0.1618 (rounded)
Arthur Has A Box Which Contains 6 Black Balls And N (n 2) White Balls, Then At Random, He Takes 3 Balls

Related Questions

PLEASE HELP!!!!!! I will give points

Answers

Answer:

Of the basketball players on the team, exactly 75% of the players have heights above 180

Step-by-step explanation:

So, they are 12 basketball players in total

1 - 170 - This is 1/12

2 - 175 - This is 1/6

1 - 180 - This is 1/12

4- 185 - This is 1/3

3 - 190 - This is 1/4

1 - 195 - This is 1/12

75% (Or 3/4) have heights above 180

Therefore, the answer is B

6. (CED.2, REI. 6) A manager is comparing
the cost of buying baseball caps from two
different companies.
Company X charges a $50 fee plus S7 per
baseball cap.
Company Y charges a $30 fee plus $9 per
baseball cap.
For what number of baseball caps will the
cost be the same at both companies?
A. 20
B. 10
C. 40
D. 100

Answers

I think the answer for this question is the second one

of 30 students, 1/3 play sports. Of those who play sports, 2/5 play soccer.
How many students play soccer?
A. 4
B.12
C.5
D.10


PLEASE HELP

Answers

It’s 4
1/3 of 30 equal 10
10 times 2/5=4

Rewrite the following without an exponent. 6^-2
Please answer ASAP!

Answers

Answer:

Rewriting [tex]6^{-2}[/tex] without an exponent we get [tex]\mathbf{\frac{1}{36}}[/tex]

Step-by-step explanation:

We need to rewrite the following without an exponent. [tex]6^{-2}[/tex]

We need to solve the exponent to find the result.

We know the exponent rule: [tex]a^{-b}=\frac{1}{a^b}[/tex]

Now using this rule to solve the equation:

[tex]6^{-2}\\=\frac{1}{6^2}\\We \:know \:that\:6^2 = 6\times 6=36\\=\frac{1}{36}[/tex]

So, Rewriting [tex]6^{-2}[/tex] without an exponent we get [tex]\mathbf{\frac{1}{36}}[/tex]

Write the given percent of increase or decrease as a growth factor.



7% Increase


a.1.7

c. 7.1

c.1.007

d.1.07

Answers

Answer: D

Step-by-step explanation:

A rectangular garden has a perimeter of 50cm. The length of one side is 15cm. What is the measurement of the width?​

Answers

Answer:

The measurement of the width is 10cm.

Marking brainliest


Stefanie has 18 grams of 20% sugar syrup and john 30 of 25% if Stefanie and john mix the syrups together how many grams of sugar will they have?

Answers

Answer:

[tex]11.1\: \mathrm{g}[/tex]

Step-by-step explanation:

Stefanie's mixture of 18 grams has a 20% sugar content. Therefore, there are [tex]18\cdot 0.2=3.6[/tex] grams of sugar in her syrup.

John's mixture of 30 grams has a 25% sugar content. Therefore, there are [tex]30\cdot 0.25=7.5[/tex] grams of sugar in her syrup.

Therefore, if they mix their syrups together, there will be [tex]3.6+7.5=\fbox{11.1}[/tex]grams of sugar.

Answer:

I need this answer ASAP

Step-by-step explanation:

19 ≥ 3f+1 ≥5 pls help

Answers

Answer:

Hi...u should do like this

18>3f>4

6>f>4/3

A student was measuring water in a graduated cylinder. The student read the amount of water at 20 ml. The actual amount of water in the graduated cylinder was 17 ml. What is the approximate percent error?
A.
3%

B.
8%

C.
15%

D.
18%

Answers

The answer is D. 18%

{[(9 + 5) ÷ 7] - 2} x [4 x (25 – 20)]

Answers

Answer:

The answer is 0.

Step-by-step explanation:

solve 9+5=14

14/7=2

2-2=0

solve the pther side

25-20=5

4*5=20

0*20=0

use one or more exponents to write the expression 9 x 9 x 9 x 9 x 7 x 7

Answers

Answer:

9^3 times 7^2

Step-by-step explanation:

solve the questions bellow

Answers

Answer:

1. 29.67°

2. 68.96°

3. 89.85°

Step-by-step explanation:

1. Reference angle = x

Opposite = 45 cm

Adjacent = 79 cm

Therefore:

[tex] tan(x) = \frac{45}{79} [/tex]

[tex] tan(x) = 0.569620253 [/tex]

[tex] x = tan^{-1}(0.569620253) [/tex]

[tex] x = 29.67 [/tex] (nearest hundredth)

2. Reference angle = B

Opposite = 14

Hypotenuse = 15

Therefore:

[tex] sin(B) = \frac{14}{15} [/tex]

[tex] sin(B) = 0.93333 [/tex]

[tex] B = sin^{-1}(0.93333) [/tex]

[tex] B = 68.96 [/tex] (nearest hundredth)

3. Reference angle = x

Adjacent = 238,900 mi

Hypotenuse = 92,955,807 mi

Therefore:

[tex] cos(x) = \frac{238,900}{92,955,807} [/tex]

[tex] x = cos^{-1}(\frac{238,900}{92,955,807}) [/tex]

[tex] x = 89.85 [/tex] (nearest hundredth)

Need help #1. The answer is shown, but I don’t know how to get to the answer. Please teach and show steps.

Answers

Answer:

B

Step-by-step explanation:

We are given that x and y are functions of time t such that x and y is a constant. So, we can write the following equation:

[tex]x(t)+y(t)=k,\text{ where $k$ is some constant}[/tex]

The rate of change of x and the rate of change of y with respect to time t is simply dx/dt and dy/dt, respectively. So, we will differentiate both sides with respect to t:

[tex]\displaystyle \frac{d}{dt}\Big[x(t)+y(t)\Big]=\frac{d}{dt}[k][/tex]

Remember that the derivative of a constant is always 0. Therefore:

[tex]\displaystyle \frac{dx}{dt}+\frac{dy}{dt}=0[/tex]

And by subtracting dy/dt from both sides, we acquire:

[tex]\displaystyle \frac{dx}{dt}=-\frac{dy}{dt}[/tex]

Hence, our answer is B.

Answer:

Let x and y be functions of time t such that the sum of x and y is constant.

(B) is the right answer

What is Four more than twice a number is -10?

Answers

4+2x=10
2x=10-4
2x=6
X=6/2
X=3

A family buys 5 airline tickets. They also buy travel insurance that is an additional $17 per ticket ($85). The total cost for the 5 tickets plus the insurance is $1,495. Let x represent the price of one ticket. Write and equation to represent the situation. *

Answers

Answer:

The first answer is 5(x+17)=1,495

The second one is $282

Hope this helps

Which row of the table reveals the y-intercept of function ? X f(x) 2 -1 0 2 1 0 2 ch -6 3 -24​

Answers

Answer:

2, -1

Step-by-step explanation: Got it right on Edge

The row of the table of the y-intercept of the function is f ( 2 ) = -6

What is a function rule?

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

Now , the value of A is

f ( -1 ) = 2^2/3

f ( 0 ) = 2

f ( 1 ) = 0

f ( 2 ) = -6

f ( 3 ) = -24

Hence , the function is f ( 2 ) = -6

To learn more about function rule click :

https://brainly.com/question/3760195

#SPJ7

help me out please. what is 5 ÷ 9/10 ?

Answers

0.5555556

I Hope This Helps! (^_^)

John is going camping, and he needs to buy a tent. The outdoor store has one that cost $90, but it's on sale for 25% off. What is the sale price?

A.$22.50
B.$65.00
C.$67.50
D.$112.50

Answers

Answer:

A

Step-by-step explanation:

Okay so, im not the best at explaining, but so we have a percentage. its 25%. you want to take the 25% and put it over 100 because a percentage is a number or ratio expressed as a fraction of 100. so it will be written as 25%/100

divide 25 by 100 and you get 0.25, correct? so that's one step further towards the answer.

then we write x/90 because we don't know (well we do) what we're gonna put. but, we're gonna multiply 0.25 by 90 and we get 22.5, which is equivalent to 22.50.

The answer is A akbdjbd d

find the product of (−x−3)(2x2+5x+8)

Answers

The product is -5x^2-27x-36
-5x-^27x-36


^=2
Hope this helps

_____consists of activities that are
not required as part of one's formal
role in the organization
Select one:
a. None of the above
b. Lobbying
c. Influence
d. Political behaviour

= Political behaviour ​

Answers

Step-by-step explanation:

political behaviour consists of activities that are

not required as part of one's formal

role in the organization

All of the following would make a formal proof incomplete except what?
A) A lack of justifications
B) Incomplete sentences
C) Errors in logic
D) Incorrect reasons for statements
Urgent I need this for tonight please!!!

Answers

Answer:

b incorrect sentences

Step-by-step explanation:

got it right on my test

Translate the verbal expression: Six times a number yields 48.

Answers

six times eight equals fourtyeight

6x8=48

The verbal expression six times a number yields 48 is translated as, 6×8=48. As a result, the number is 8.

What is an expression?

It is defined as the combination of constants and variables with mathematical operators. A mathematical situation can be expressed verbally as a condensed version. It describes the connections and operations that take place between quantities.

It is given that the verbal expression is six times a number yields 48.

Suppose the number is x,

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

The expression is translated as,

6×8=48

Thus, the verbal expression six times a number yields 48 is translated as, 6×8=48. As a result, the number is 8.

Learn more about the expression here:

brainly.com/question/14083225

#SPJ6

Question 9 Multiple Choice Worth 1 points) (03.01 MOO) 13 Simplify​

Answers

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{\frac{ \sqrt[4]{ \\ 3} }{ \sqrt[5]{3} } }[/tex]

Note : For a problem like this, all we have to do is Rewrite the problem in exponential form to give us an answer of :

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ {_3}\cfrac{1}{20} }[/tex]

[tex]\therefore[/tex]The correct part of the problem is A) [tex] \bold{ {_3}\cfrac{1}{20} }[/tex]

A surf shop charges $6 to rent a wetsuit and $12 per hour to rent a surfboard. Write a function to model the cost, c, to rent a wetsuit and surfboard for h hours.

Answers

Answer:

c(h)=12h+6

because the swimsuit only needs to be paid for once, whereas the surfboard is charged on an hourly basis

I WILL GIVE BRAINLIST AND 50 POINTS
The students in a class made graphs to keep track of the number of pages they read in their books.

Which graph shows a proportional relationship?
A.
B.
C.
D.

Answers

Step-by-step explanation:

A proportional relationship graph would show that the points can be arranged in a line that passes through the origin.

All of the points in Graphs B, C and D cannot be connected in 1 straight line, hence they are not proportional relationships.

Only Graph A shows a proportional relationship.

Answer:

a

Step-by-step explanation:

Please solve the question below 4

Answers

Answer:

The answer is C

Step-by-step explanation:

The graph has a normal distribution, mean at 3.6, and a standard deviation of 0.6

Answer:

the Correct Answer Is c

Step-by-step explanation:

PLZ PLZ PLZ MARK AS BRAINLIEST LOL PLZ

(help me it is not much)
Which form of a linear equation should we use when given the y-intercept and the slope of
the line?
Point-Slope form
Slope-intercept form
Standard form?

Answers

Answer:

Slope Intercept Form

Step-by-step explanation:

its the basics

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 429.0429.0 gram setting. It is believed that the machine is underfilling the bags. A 4040 bag sample had a mean of 425.0425.0 grams. A level of significance of 0.020.02 will be used. Determine the decision rule. Assume the standard deviation is known to be 11.011.0.

Answers

Answer:

A 4040 bag sample 25.0425.0 grams. A level of significance of 0.020.02

the decision rule. Assume the standard deviation is known to be 11.011.0.

Step-by-step explanation:

The following inequality has a solution in the form X > A. Solve the inequality and place the correct value of A into the box.

-17x - 10 > 7 - 20x

Answer: x > ______
Enter your answer as an integer or a reduced fraction in the form A/B.

Answers

It is the answer 20 x of that

A stockbroker knows from experience that the probability that a client owns stocks is 0.60. P(A) The probability that a client owns bonds is 0.50. P(B) The probability that the client owns bonds if he/she already owns stock is 0.55 What is the probability of a client owning stocks OR bonds

Answers

Answer:

the probability of a client owning stocks OR bonds is 0.825

Step-by-step explanation:

The computation of the probability of a client owning stocks OR bonds is given below:

= P(stocks) + P(bonds) - P(stocks and bonds)

= 0.60 + 0.50 - (0.55 × 0.50)

= 0.60 + 0.50 - 0.275

= 0.825

Hence, the probability of a client owning stocks OR bonds is 0.825

Other Questions
plz answer my latest question i really need help so plz Guys, I have sooo much schoolwork. Why is it when the last couple of days left in the semester do they decide to give us all the work then? Im stressing over this sooo much its not even funny. And if i dont get it done then im screwed. go ahead take my points ak for brainliest not like ppl on here really care anyways. they just want the points and stuff to themselves they dont actually want to help othersss. BRAINLEIST Using the graph below, find the missing value to complete the t-chart.x y-3 50 -12 ?A.5B.-3C.-5D.3 A college campus has a lawn shaped like a circle with a radius, r, of 60 meters. Which is the best approximation of the area, A, of the circular lawn? (Use A=r2; is approximately 3.14.) PLEASE HELP I WILL GIVE BRAINLIEST!! I NEED HELP FAST Choose the correctly punctuated sentence *Pardon me, urged Erlinda. Can you watch my children for a moment while I answer my cell phone?Pardon me, urged Erlinda. can you watch my children for a moment while I answer my cell phone?Pardon me, urged Erlinda. Can you watch my children for a moment while I answer my cell phone? plz answer ? below ty Determine the lateral and total surface area of the pyramid. the base of a parallelogram is 2more than the height The area of the parallelogram is 120yd^2, find the base and the height 1pt Twins raised in different families still exhibit similar mannerisms, indicating that at least some behavior isO A. genetisOB. environmentalO C. instinctualOD. learned 1. Q1) Which number is missing from this prime factortree? Meiji Isetan Corp. of Japan has two regional divisions with headquarters in Osaka and Yokohama. Selected data on the two divisions follow: Division Osaka YokohamaSales $3,000,000 $9,000,000Net operating expenses $210,000 $720,000Average operating assets $1,000,000 $4,000,000Required:a. For each divisions, compute the return on investment (ROI) in terms of margin and turnover. (Do not round intermediate calculations.)b. Assume that the company evaluates performance using residual income and that the minimum required rate of return for any division is 15%. Compute the residual income for each division. What's the answers to Part A and Part B? What is the minimum, First Quartile (Q1), Median, Third Quartile, Maximum for 5,6,8,8,9,10,13,14,16,16,16,18,19, 21,22,23,25 of the data set? Which best explains why Great Britain, France, and Russia formed the Triple Entente?They hoped to help each other imperialize Africa and counter the power of the Triple Alliance on that continent.They feared the rising military power of Germany and sought to counter the power of the Triple Alliance.They wanted to prevent conflict in the Balkans and convince the Triple Alliance not to interfere in the region.They sought to surround Germany on two sides and convince the Triple Alliance not to expand its power. Why did the US and USSR never declare war on one another?(A) Neither country wanted to engage in a nuclear war that would lead toworldwide destruction(B) The US was concerned about having to enter a war with all of the EasternBloc countries(C) The USSR was concerned about having to enter war with all of the WesternBloc countries(D) All of the answer choices In his 2011 State of the Union Address, President Barack Obama said:"To attract new businesses to our shores, we need the fastest, most reliable ways to move people, goods, and informationfrom high-speed rail to high-speed Internet. Our infrastructure used to be the best, but our lead has slipped. The jobs created by the transcontinental railroad & the Interstate Highway System didn't just come from laying down track or pavement. They came from businesses that opened near a town's new train station or the new off-ramp.We've begun rebuilding for the 21st century. And tonight, I'm proposing that we redouble those efforts. We'll put more Americans to work repairing crumbling roads and bridges. Within 25 years, our goal is to give 80% of Americans access to high-speed rail. Within the next five years, we'll make it possible for businesses to deploy the next generation of high-speed wireless coverage to 98% of all Americans. This isn't just about faster Internet or fewer dropped calls. It's about connecting every part of America to the digital age."Is this excerpt from President Obamas speech an example of argument or persuasion? Provide at least two reasons to support your answer. Answer in complete sentences.please help 100points!!!!And I will make brainiestonly if there is a good explanation. Fill in with the correct definite article and tell if the word is masculine or feminine , singular or plural. Ex. ___perro. El perro - masculine, singular. One week, Paige earned $165.75 at her job when she worked for 13 hours. If she is paid the same hourly wage, how many hours would she have to work the next week to earn $318.75? Why do many people believe that the Earth is flat if it is actually round? what is m1 if m7 = 60?