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

solve for y.
-13=4y+3​

Answers

Answer:

-13=4y+3 -3

-16=4y ÷4

-4=y

Step-by-step explanation:

hope it helps ^^

Answer:

y = -4

explenation in picture

What is 2/3-5/9 in 5th grade math

Answers

Answer:

0.111111

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solution

=2×3/3×3-5×1/9×1

=6/9-5/9

=6-5/9

=1/9

Please mark me brainliest.Ok

It takes 3 gallons of gas to drive 102 miles. How many miles can be driven on 16 gallons of gas?

Answers

Answer:

544

Step-by-step explanation:

102 divided by 3 to find how many miles per gallon which is 34 then multiply by 16

Answer:

544

Step-by-step explanation:

102 divided by 3 to find how many miles per gallon which is 34 then multiply by 16 which is 544.

Write as a product - 12a+12
DONT ANSWER QUESTION IF U DONT KNOW

Answers

Answer:

24a no>?

Step-by-step explanation:

A production company spent 45
1
2 days filming its first movie. The​ company's second movie was filmed in 7
3
4 weeks. Find the ratio of the first​ movie's filming time to the second​ movie's filming time. Compare in weeks.

Answers

Answer:

26 /33

Step-by-step explanation:

Given that :

Number of days taken filming first movie = 45 1/2

Number of weeks spent filming second movie = 8 1/4

Concerning days to weeks ;

45 1/2 days = 91/2 days = 91/2 ÷ 7 ;

91 / 2* 1/7 = 91/14 = 6. 5 weeks

Hence,

Ratio of first week fuming to second week filming ;

6.5 weeks : 8 1/4 weeks

6 1/2 : 8 1/4

13 / 2 : 33 /4

13 / 2 * 4 /33

52 / 66

26 / 33

A rectangle has a perimeter of 50 centimeters. If the width of the rectangle is 10 centimeters, what is its length?​

Answers

Answer:

15 cm

Step-by-step explanation:

The perimeter of a rectangle is 2(L + W), where L is length of the rectangle and W is the width.

If we plug in 10 for W, we get this:

2L + 2(10) = 50 <-- the perimeter

2L + 20 = 50

2L = 30

L = 15

aight can someone help me lol

Answers

It’s gonna be -1/8 correct me if I’m wrong:)


One side of a triangle is 3 times the second side. The third side is 17 feet longer than the second side. The perimeter of a
triangle is 52 feet. Find the length of each side.

Answers

Answer:

Side 1=21 ft, Side 2=7, Side 3=24

Step-by-step explanation:

52 = (3x) + (x) + (x+17) -> 52 = 5x + 17 -> 5x = 35 -> x = 7

Plus 7 into the equation whenever you see an x.

help please and u get a cookie

Answers

Answer:

im allergic to cookies

Step-by-step explanation:

What is the value of a2 + 36 2c when a = 3, b = 8, and c = 2?​

Answers

Answer: 21 +4c

Step-by-step explanation:

Answer:

what is in between 36 and 2c?

You spin the spinner and flip a coin. Find the probability of the compound event. The probility of spinning one, and landing on heads is:

Answers

Answer:

You have to specify the question more. There's not enough information. Like how many numbers does the spinner have? I'll help if you could specify it more

Step-by-step explanation:

Answer:

Multiply 1/2 by 1/5 and you get 1/10

Step-by-step explanation:

help please !!! x/4 = 9/x

Answers

Step-by-step explanation:

x/4=9/x

x.x=4.9

x^2=36

√x=√6

x=6

A political action committee wanted to estimate the proportion of county residents who support a change to the county leash law. They took a random sample of 600 county residents and found that the proportion who wanted to change the law was 33% with a margin of error of +/- 4% (with 95% confidence). This implies:_____

a. If we took another sample of 600 residents the sample proportion would definitely be between 29% and 37%.
b. If we take many other samples from this population 95% of them will have a sample proportion that is between 29% and 37%.
c. We can not conclude anything about the population parameter since this is only a sample.
d. We are 95% confident that the true proportion of county residents who want the law changed is between 29% and 37%.
e. There is a 95% chance that the true parameter is 33%.

Answers

Answer:

d. We are 95% confident that the true proportion of county residents who want the law changed is between 29% and 37%.

Step-by-step explanation:

Meaning of a confidence interval:

A x% confidence interval being between a and b means that we are x% sure that the true population proportion is between a and b.

In this question:

Sample of 600, proportion who wanted to change the law was 33% with a margin of error of +/- 4% (with 95% confidence). This implies:

From the concept of confidence interval above, the correct answer is:

d. We are 95% confident that the true proportion of county residents who want the law changed is between 29% and 37%.

If Log 20 = 1.301 what is the value of Logsub100 20?

I need the step by steps! I can’t find anything videos online to teach this to me

Answers

Answer:

[tex]log_{100}20 = 0.6505[/tex]

Step-by-step explanation:

log20 = 1.301 (when you see only "log" with no base, it is taken as a base 10)

This basically means:

[tex]10^{1.301} = 20[/tex]  (This is the log in exponential form)

Since we don't know what  [tex]log_{100}20[/tex]  is equal to, we will say  [tex]log_{100}20[/tex] = x

So to solve for [tex]log_{100}20[/tex] = x, you do the same thing. (convert to exponential form)

[tex]100^{x} =20[/tex]

Now you will notice that both of these equations are equal to 20.

Since 20 = 20,

we can say [tex]100^{x}[/tex] = [tex]10^{1.301}[/tex]

Another way of saying 100, is [tex]10^{2}[/tex] (make the bases the same)

Now we get [tex]10^{2x} = 10^{1.301}[/tex]      

(we get 2x because an exponent to the power of an exponent ([tex]2^{x}[/tex]) is the same as 2 * x)

Because you have the same base, you can just ignore the 10s and focus on the exponents. So you get:

2x = 1.301

x = 0.6505

Problem: 2 - $(7 – 2y) = -3
Step 1: -3(7 2y) = -3
Step 2: -21 + 6y=-3
Step 3: by = 18
Step 4: y = 3
Determine which number step the mistake is Made and describe the error

Answers

Step 3. Instead of subtracting -21 and -3, they should’ve added because they are like terms. A negative plus a negative is still a negative.

Ms. Davis is doing an activity with her statistics students where she gives them a 202020-question multiple choice test, and they know none of the answers. Students need to guess on every question, and each question has 555 possible choices, 111 of which is correct.
What are the mean and standard deviation of the number of questions that each student gets correct?
You may round your answers to the nearest tenth.

Answers

Answer:

The mean and standard deviation of the number of questions that each student gets correct are 4 and 1.789 respectively (

Answer: mean: 4

standard deviation: 1.79

Step-by-step explanation:

Over the holiday break, Ms. Horton baked a ham that was 19 1/4 pounds.
By the end of the night there was 6 7/10 pounds left. How much turkey was
eaten that night?

Answers

Answer:

12 11/20

Step-by-step explanation:

the answer to the question is 12 11/20

Simplify QP
R ( 0 , a )
S ( b , c )
Q ( 0 , -a )
P ( b , -c )

Answers

Answer:

b² + ( -c + a ) ²

Step-by-step explanation:

The quotient of dividing a number by 4 is 5. Find the number.​

Answers

Answer: 20

Step-by-step explanation:

A quotient is th value that is gotten when two numbers are divided. Based on the information given in the question, let the number be represented by x.

Therefore, x/4 = 5

x = 4 × 5

x = 20

The number is 20

Alex drew the triangles shown. Which of the following correctly describes the triangles?

Answers

Answer: wheres the attachment..

Step-by-step explanation:

You would like to buy new carpet for a room. The room us rectangular. The dimensions are 12 1/3 feet by 10 3/4 feet. How many square feet of carpet do you need?

Answers

It’s about 132.58 square feet also you should ask if your are rounding up or not if so it should be 132.60

Which equation describes the pattern of the data in the table?
Х
3
4 5 6 7
12 16 20 24 28
у
A y = 4x
B y = 4x+12
1
y = -X
1 x +12
D
4

Answers

Answer:

Option A. y = 4x

Step-by-step explanation:

From the question given above, the following data were obtained:

X >> Y

3 >> 12

4 >> 16

5 >> 20

6 >> 24

7 >> 28

Next, we shall use each of the options to obtain the first two value of y to which will correspond to the table above. This is illustrated below:

For Option A:

1. y = 4x

x = 3

y = 4 × 3

y = 12

2. y = 4x

x = 4

y = 4 × 4

y = 16

For Option B:

1. y = 4x + 12

x = 3

y = 4(3) + 12

y = 12 + 12

y = 24

2. y = 4x + 12

x = 4

y = 4(4) + 12

y = 16 + 12

y = 28

For Option C:

1. y = ¼ x

x = 3

y = ¼ × 3

y = ¾

2. y = ¼ x

x = 4

y = ¼ × 4

y = 1

For Option D:

1. y = ¼x + 12

x = 3

y = ¼(3) + 12

y = ¾ + 12

y = 51/4

2. y = ¼x + 12

x = 4

y = ¼(4) + 12

y = 1 + 12

y = 13

From the calculations made above, only option A ie. y = 4x correspond to the data given in the table above.

Please I really need help on this one

Answers

Answer:

2.5ft

Step-by-step explanation:

d=2r

r=1/2d

r=1/2*5ft=2.5 ft

6) Find the distance between -8 and 10.
) What is an expression that represents the
distance? Complete the expression.
1
-8
10
1
- 10 -8
What is the distance?
?
units

Answers

the distance is 18 units and the equation would be (-8 - 10)


The elevation at ground level is 0 feet. An elevator starts 90 feet below ground level. After traveling for 15 seconds, the elevator is 20 feet below ground level. Which statement describes
the elevator's rate of change in elevation during this 15-second interval?

Answers

Answer:

elevator travel 4.5 feet per second

Answer: A

Step-by-step explanation:

the answer is A

what is 4 divided by 8464

Answers

0.00047258979206 .....

Answer:

4 divided by 8464 equals 0.00047258979

8464 divided by 4 equals 2,226

Step-by-step explanation:

                May I have brainiest I'm trying to level up!

                                  </3 PureBeauty

You are doing research on balance and fitness. To complete this research you will need a watch with a second hand. Identify a random sample of n = 12 men and n = 8 women. You must answer this question: How do you establish that this sample is truly random?

Answers

Answer:

Step-by-step explanation:

In order to establish that the sample is truly random you need to obtain two main factors. First, is making sure that the random sample of both groups chosen (men and women) are equal in proportion to the overall population. Meaning both groups must be the same percentage of the overall population of the same gender. The second factor that you need to make sure of is that all chosen individual's had the exact same probability of being chosen from the population and no external factor influenced the probability of them being chosen for the study.

Can anyone please help me please

Answers

Answer:

this isnt spanish

Step-by-step explanation:

Between the 4 and 9 is 11
Under 4 is 15
Under 9 is 20

A person invested $30,000 in stocks and bonds. Her investment in bonds is $3000 more than half her investment in stocks
How much did she invest in stocks? How much did she invest in bonds?

Answers

Answer:

He invested in stocks Say,  = x $

 He invested in bonds = (x/2)+6000

 So,

 x+ x/2 +6000=30000

 2x+x+12000=60000

 3x= 48000

x=16000

 Investment in stocks= 16000  $

Step-by-step explanation:

!!

Answer:

      $ 3 0 , 0 0 0  in Stocks

       $ 2 7 , 0 00  in Bonds

Step-by-step explanation:

        $ 3 0 , 0 0 0

      - $ 3 , 0 0 0

  _  _ _ _ _ _ _ _ _ _

         $ 2 7 , 0 0 0

Working out Choose a person aged 19 to 25 years at random and ask, "In the past seven days, how many times did you go to an exercise or fitness center or work out?" Call the response Y for short. Based on a large sample survey, here is a probability model for the answer you will get:8Working out Choose a person aged 19 to 25 years at random and ask, "In the past seven days, how many times did you go to an exercise or fitness center or work out?" Call the response Y for short. Based on a large sample survey, here is a probability model for the answer you will get:8

Answers

Solution :

Days :              0           1        2         3         4          5        6         7

Probability : 0.68     0.05   0.07   0.08   0.05    0.04   0.01    0.02

This is a valid probability distribution.

In the question it is given that call for a response of Y for short of a sample of people aged between 19 years to 25 years.

Also the event that describes the value of call for response greater than 3 i.e. (Y < 3) is a randomly chosen people between the age 19 to 25 years old who has gone to fitness center or did exercise fewer than 3 days.

Valid probability models add up to 1

The probability is a valid probability model

The probability model is given as:

Days :              0           1        2         3         4          5        6         7

Probability : 0.68     0.05   0.07   0.08   0.05    0.04   0.01    0.02

To determine if the model is a valid probability model, or not

We make use of:

[tex]\mathbf{\sum P(x) = 1}[/tex]

So, we have:

[tex]\mathbf{0.68 + 0.05 + 0.07 + 0.08 + 0.05 + 0.04 + 0.01 + 0.02 = 1}[/tex]

Add the probabilities

[tex]\mathbf{ 1= 1}[/tex]

The above equations shows that:[tex]\mathbf{\sum P(x) = 1}[/tex]

Hence, the probability is a valid probability model

Read more about probability models at:

https://brainly.com/question/9965602

Other Questions
Simplify QP R ( 0 , a ) S ( b , c ) Q ( 0 , -a ) P ( b , -c ) Adolf Hitler and the Nazi party came to power during the German depression. Why were Hitler and Nazism so appealing to Germans in the 1930s? Social learning suggests that children who grow up in homes where violence is a way of life may learn to believe that such behavior is acceptable.A. TrueB. False QUICK I WILL GIVE U BRAINLIEST!!!! Read this stanza from "The Raven" by Edgar Allan Poe.Once upon a midnight dreary, while I pondered, weak and weary,Over many a quaint and curious volume of forgotten loreWhile I nodded, nearly napping, suddenly there came a tapping,As of some one gently rapping, rapping at my chamber door."'Tis some visitor," I muttered, "tapping at my chamber doorOnly this and nothing more."How does what happens in this stanza propel the action in the poem?It gives the speaker a reason to speak to the raven.It introduces the story and sets up the coming events.It resolves the main conflict of the story.It establishes why Lenore has left the speaker alone. Georgia's entrepreneurs worked to move the state away fromEntrepreneurs try to make more money than they spend, which is known as making an)The possibility of losing a business is one of the of entrepreneurshipThe creation of new jobs and opportunities is one of the y of entrepreneurship One side of a triangle is 3 times the second side. The third side is 17 feet longer than the second side. The perimeter of atriangle is 52 feet. Find the length of each side. Susan's job involves recruiting eligible people for a business. It's her responsibility to identify the task requirements and then recruit candidates to fill the vacancy. Which management function is Susan performing? A production company spent 4512 days filming its first movie. The company's second movie was filmed in 734 weeks. Find the ratio of the first movie's filming time to the second movie's filming time. Compare in weeks. what is the slope of the line that passes through the pair of points. (1,7) , (10 ,1) A dolphin travels a distance 20 miles up the coastline in 153 minutes. If 1 mile is equal to1609 meters, then what is the dolphin's average speed in meters/second rounded to thenearest tenth?+/-HELP ME PLEASE what are the steps for solving 6x-1=-x+9 Which phrase became popular after passage of the Stamp Act the Embargo Act of 1807 was passed by Congress under the President Thomas Jefferson to stop all trade between America and any other country to goal was to If Log 20 = 1.301 what is the value of Logsub100 20?I need the step by steps! I cant find anything videos online to teach this to me Pls help and show workings Thank you in advance Option A. 7B. 10C. 13D. 22 why does tilly pull over when chasing goldfinger?A. Her car engine stopsB. She is mad a BondC. Bond slashes her tireD. She thinks Bond is interfering A political action committee wanted to estimate the proportion of county residents who support a change to the county leash law. They took a random sample of 600 county residents and found that the proportion who wanted to change the law was 33% with a margin of error of +/- 4% (with 95% confidence). This implies:_____a. If we took another sample of 600 residents the sample proportion would definitely be between 29% and 37%.b. If we take many other samples from this population 95% of them will have a sample proportion that is between 29% and 37%.c. We can not conclude anything about the population parameter since this is only a sample.d. We are 95% confident that the true proportion of county residents who want the law changed is between 29% and 37%.e. There is a 95% chance that the true parameter is 33%. I need help its urgent please I would really appreciate it 1.) Determine if the coordinate points represent a function. (1.3). (2.6). (3.9). (4. 12). (5.15 O Function O Not a FunctionO both Why my video ads are not working ?