Two players take turns removing a ball from a jar that initially contains m white and n black balls. The rst player to remove a white ball wins. Find the probability that the starting player wins.

Answers

Answer 1

½×½ which will be ¼

Step-by-step explanation:

because

Answer 2

Probability that the starting player wins:

[tex]P_{n} =[/tex]  m /n + m + n(n-1) /(n + m)(n+m -1) × [tex]P_{n-2}[/tex]

Let us say that the probability that the first player wins is [tex]P_{n}[/tex]. Then this can be happen in two ways:

If the first player wins in the first move which has a probability: m /n + m

If the first player wins after the second move which has a probability :

n(n-1) /(n + m)(n+m -1) × [tex]P_{n-2}[/tex]

Therefore by the law of probability,

[tex]P_{n} =[/tex]  m /n + m + n(n-1) /(n + m)(n+m -1) × [tex]P_{n-2}[/tex]

This will allow us to find out the probability of first player winning the game recursively.

Know more about probability,

https://brainly.com/question/31828911

#SPJ2


Related Questions

Please help!!!!!!!!!!!asap

Answers

By solving y = 25 · x² - 100 through the square root method, we conclude that the two roots of the quadratic formula are y₁ = + 2 and y₂ = - 2.

How to obtain the roots of a second order polynomial

Herein we have a polynomials of the form y = a · x² - b. By algebra we find that two roots exists, which are described below according to the square root method:

[tex]y_{1} = +\sqrt{\frac{b}{a} }[/tex], [tex]y_{2} = -\sqrt{\frac{b}{a} }[/tex]

If we know that a = 25 and b = 100, then the two roots of the equation are:

y₁ = + 2, y₂ = - 2

By solving y = 25 · x² - 100 through the square root method, we conclude that the two roots of the quadratic formula are y₁ = + 2 and y₂ = - 2.

To learn more on quadratic equations: https://brainly.com/question/2263981

#SPJ1

Mr. McMillan and Ms. Burke are teaching their classes how to write in cursive. Mr. McMillan has already taught his class 8 letters. The students in Ms. Burke's class, who started the unit later, currently know how to write 12 letters. Mr. McMillan plans to teach his class 4 new letters per week, and Ms. Burke intends to cover 3 new letters per week. Eventually, the students in both classes will know how to write the same number of letters. How long will that take? How many letters will the students know?

Answers

The number of weeks by which the students in both classes will know how to write the same number of letters will be 4 weeks.

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Mr. McMillan and Ms. Burke are teaching their classes how to write in cursive.

Mr. McMillan has already taught his class 8 letters.

The students in Ms. Burke's class, who started the unit later, currently know how to write 12 letters.

Mr. McMillan plans to teach his class 4 new letters per week.

Ms. Burke intends to cover 3 new letters per week.

Eventually, the students in both classes will know how to write the same number of letters.

Then the number of weeks by which the students in both classes will know how to write the same number of letters will be

Let x be the number of the weeks and y be the total number of the letters.

Then the equation will be

y = 4x + 8 …1

y = 3x + 12 …2

Then by solving the equations 1 and 2, we have

x = 4 and y = 24

More about the linear system link is given below.

https://brainly.com/question/20379472

#SPJ1

Do this for me pls its mdths

Answers

Answer:

A = -1

B = -3

C = -7

Step-by-step explanation:

See attached image.

Toby has five coins. Three of the coins add up to 30p. Three of the coins add up to 40p. All the coins add up to 50p. List Tony's coins in ascending order of value.

Answers

Tony's coins in ascending order of value will be 5p, 10p, and 15p.

Definition of in Ascending order

Arranged in a series that begins with the smallest or least and ends with the largest or greatest The children were lined up in ascending order of height. Test score are listed in ascending order from lowest to highest.

How do depict the information?

Based on the information given, the values of the coins will be 5p, 5p, 10p, 15p, and 15p.

In this case, 5p + 10p + 15p = 30p

10p + 15p + 15p = 40p

5p + 5p + 10p + 15p + 15p = 50p

Therefore, Tony's coins in ascending order of value will be 5p, 10p, and 15p.

Learn more about coins on: brainly.com/question/2974216

#SPJ10

Match the verbal expression (term) with its algebraic expression (definition).

Match Term Definition
d
Some number increased by two A) a ÷ 2
c
A variable decreased by two B) y2
e
Product of an unknown value and two C) x − 2
2
Quotient of some number and two D) b + 2
b
An unknown value squared E) 2z

Answers

The matching of definitions and terms are done below.

Some number increased by two ⇒ b + 2A variable decreased by two ⇒ x – 2Product of an unknown value and two ⇒ 2zQuotient of some number and two ⇒ a ÷ 2An unknown value squared ⇒ y²

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Match the verbal expression (term) with its algebraic expression (definition).

Some number increased by two ⇒ b + 2

A variable decreased by two ⇒ x – 2

Product of an unknown value and two ⇒ 2z

Quotient of some number and two ⇒ a ÷ 2

An unknown value squared ⇒ y²

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1

Your family is driving to Disney which is 1000 miles away The first day your family drives 600 miles in 10 hours and the second day they drive the remaining distance in 8 hours . What is the average speed of travel for the second day?

Answers

Answer:

50 miles per hour

Step-by-step explanation:

Step 1: We subtract 600 from 1000. That gives us 400 miles for the second day.

Step 2: Now we divide that by 8, giving us 50 miles per hour. We have our answer!

I hope this helped!! PLEASE MARK AS BRAINLIEST!! :)

A boat leaves a dock and goes 240 miles in a direction of 290 degrees. It then turns and goes 50 miles in a direction on 30 degrees. How far is the boat from the dock and in what direction?

Answers

By Pythagorean theorem and trigonometric functions, the magnitude and direction of the boat are approximately 284.403 miles and 295.043° with respect to the east.

What is the direction and magnitude of the resulting displacement with respect to the origin

In this problem we assume that the first angle is measured with respect to the east side and that the second angle is counterclockwise and measured with respect to the direction of the first vector. First, we need to determine the resulting vector by using trigonometric and vectorial formulas:

(x, y) = (240 · cos 290°, 240 · sin 290°) + (50 · cos 320°, 50 · sin 320°)

(x, y) = (120.387, - 257.666) [mi]

The magnitude is found by Pythagorean theorem:

[tex]r = \sqrt{(120.387\,mi)^{2}+(-257.666\,mi)^{2}}[/tex]

r ≈ 284.403 mi

The direction of the boat is obtained by inverse trigonometric functions:

θ = tan⁻¹ (- 257.666/120.387)

θ ≈ 295.043°

By Pythagorean theorem and trigonometric functions, the magnitude and direction of the boat are approximately 284.403 miles and 295.043° with respect to the east.

To learn more on vectors: https://brainly.com/question/13322477

#SPJ1

If a_1=9a
1

=9 and a_n=-3a_{n-1}a
n

=−3a
n−1

then find the value of a_5a
5

.

Answers

A geometric series is the collection of an unlimited number of terms with a fixed ratio between them. The value of a₅ is -729.

What is geometrical series?

A geometric series is the collection of an unlimited number of terms with a fixed ratio between them.

Given the value of a₁=9 and the value of [tex]a_n=-3a_{(n-1)}[/tex]. Therefore, the value of a₅ can be written as,

a₂ = -3(a₁) = -3(9) = -27

a₃ = -3(a₂) = -3(-27) = 81

a₄ = -3(a₃) = -3(81) = -243

a₅ = -3(a₄) = -3(-243) = -729

Hence, the value of a₅ is -729.

Learn more about Geometrical Series:

https://brainly.com/question/4617980

#SPJ1

simplify (6 to the power of 5)power 2

Answers

Answer:

60466176

Step-by-step explanation:

HELP !!!
Which of the following best describes the slope of the line below?
• A. Negative
O B. Zero
• C. Positive
D. Undefined

Answers

The answer to this is negative

please help i dont know how to do this

Answers

First you have to do the ones in the brackets

Please Help
What does the missing angle in the triangle measure?

Answers

Answer:

x = 60

Step-by-step explanation:

The sum of the angles of a triangle is 180

95+25 +x = 180

120 +x = 180

Subtract 120 from each side

120+x-120 = 180-120

x = 60

Which of the following is equivalent to the expression?

Answers

Answer:

d

Step-by-step explanation:

- 5 (3x - 7) ← multiply each term in the parenthesis by - 5

= - 15x + 35

Answer: d.) -15x + 35

Given expression:

⇒ -5(3x - 7)

Apply distributive method: a(b + c) = ab + ac

⇒ -5(3x) -5(-7)

multiply the variables

⇒ -15x + 35

Examine the nuclear reaction: superscript 1 subscript 1 h plus superscript 1 subscript 0 n right arrow superscript 2 subscript 1 h.. why is this classified as a nuclear reaction rather than a chemical reaction?

Answers

The given reaction is considered as nuclear reaction instead of chemical reaction as the change is coming in the nucleus.

A nuclear reaction is one in which the number of protons or neutrons changes as a result of collisions between two nuclei or an atom and a subatomic particle.

In the given reaction also which is superscript 1 subscript 1 h plus superscript 1 subscript 0 n right arrow superscript 2 subscript 1 h.

A neutron is added to the nucleus of a hydrogen atom here. As a result, it is a nuclear reaction.

A chemical reaction involves the acquisition or loss of electrons, which leads in the synthesis of a new molecule while leaving the nucleus of an atom unchanged.

Thus, we can give a conclusion that because a change in a nucleus happened, the described event is categorised as a nuclear reaction rather than a chemical reaction.

Learn more about Nuclear Reactions here:

https://brainly.com/question/984564

#SPJ10


Match each inequality to the number line that represents its solution:

Answers

Step-by-step explanation:

I have solve all the questions and your work is to match with that option

Horizontal lines n and m are intersected by lines q and p. At the intersection of lines q and n, the uppercase right angle is angle 4. At the intersection of lines q and m, the uppercase left angle is angle 1. At the intersection of lines p and n, the bottom left angle is angle 3. At the intersection of lines p and m, the uppercase left angle is angle 2.

If angle 1 is 110°, what would the other angle measures have to be in order for m || n and
q || p?



Angle 2 = °



Angle 3 = °



Angle 4 = °

Answers

The values of the angles based on the information will be:

Angle 2 = 110°Angle 3 = 70°Angle 4 = 70°

How to calculate the angles?

From the information given, angle 1 is 110° and the horizontal lines n and m are intersected by lines q and p.

In this case, it should be noted that opposite angles are equal. Hence, angle 2 is also 110°.

Angle 3 will be:

= 180° - 110° = 70° (angle on a straight line).

Angle 4 will also be 70° as opposite angle to angle 3.

Learn more about angles on:

brainly.com/question/25716982

#SPJ1

which statement is true about fiction ​

Answers

Answer:

The function is even because of symmetry over x axis

A middle school took all of its 6th grade students on a field trip to see a play. The
students filled 341 seats, which was 55% of the total number of seats in the theater.
How many total seats were in the theater?

Answers

Answer: 620 seats

341/0.55 = 620

Please Help Me Answer These

Answers

Answer:

Question 1 : -2 3/4 × 3 1/5 . Change the fractions to improper fraction and multiply .

= -11/4 × 16/5

= -176/20

= -44/5

= -8 4/5

Question 1 answer : -8 4/5

Question 2: -4.6/-2

= -4.6/-2

= 2.3

Question 2 answer : 2.3

Question 3: - 7/8 ÷ (-2)(-4)

= 7/6(-4)

= -7/4

Question 3 answer : -7/4

Question 4 : -4 27/30

= -147/30

= -4.9

Question 4 answer : c

Question 5 : -3 13/20

Question 5 answer : -3.65

Therefore The answer are -8 1/4 , 2.3 , -7/4 , c , -3.65

Choose any set of Pythagorean triplets of your choice and illustrate them using graph sheet.
Example given below:

Answers

The required Pythagorean triplets are hypotenuse, perpendicular and base is 13, 12 and 5 respectively.

What are Pythagorean triplets?  

In a right angled triangle, its side, such as hypotenuse, perpendicular and base  is Pythagorean triplets.

We have

Hypohypotenuse = 13
perpendicular = 12
base = 5
Which satisfies the condition of the Pythagorean theorem.

[tex]a^2+b^2=c^2\\12^2+5^2=c^2\\169=c^2[/tex]

and c = 13

Thus, the required value of Pythagorean triplets satisfies the Pythagorean theorem.  

Learn  more about Pythagorean triplets here:
https://brainly.com/question/22160915

#SPJ1
 

 

What is the solution to the following equation?
3(x-4)-5-x-3
A. x = 12
B. x=3
C. x=8
D. x = 7

Answers

Answer:

D. x = 7

Step-by-step explanation:

NOTE : there should be an equal sign somewhere in the given expression.

suppose the equation is the following:

3(x-4)-5 = x-3

………………………………………………………

3(x - 4) - 5 = x - 3

⇔ 3x - 12 - 5 = x - 3

⇔ 3x - 17 = x - 3

⇔ 3x - 17 + 17= x - 3 + 17

⇔ 3x = x + 14

⇔ 2x = 14

⇔ x = 14/2

⇔ x = 7

What is 9 squared?
Why?
Why do we call this "Squared"?
What is 5 cubed?
Why?
Why do we call this "Cubed"?

Answers

Answer:

The squared root of 9 is 3

Why - Half of 9 is 3

Why do we called this squared - It is the positive solution of the equation x2 = 9. The number 9 is a perfect square.

5 Cubed is equal to 125

Why - The number 125 on prime factorization gives 5 × 5 × 5. On combining the prime factors in groups of 3 gives 5

Why do we call this cubed = The cube of a number is that number times itself times itself. 5 cubed, denoted 53, is equal to 5×5×5, or 125.

Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.

2.3p – 10.1 = 6.4p – 4
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
23p – 101 = 65p – 40 – p
2.3p – 14.1 = 6.4p – 4

Answers

Answer:

2.3p – 10.1 = 6.49p – 4  [tex]\huge \checkmark[/tex]

230p – 1010 = 650p – 400 – p  [tex]\huge \checkmark[/tex]

Step-by-step explanation:

……………………………………………

2.3p – 10.1 = 6.5p – 4 – 0.01p

⇔ 2.3p – 10.1 = (6.5p – 0.01p) – 4

⇔ 2.3p – 10.1 = (6.5 – 0.01)p – 4

⇔ 2.3p – 10.1 = (6.49)p – 4

⇔ 2.3p – 10.1 = 6.49p – 4

_______________________

_______________________

2.3p – 10.1 = 6.5p – 4 – 0.01p

⇔ 100 × (2.3p – 10.1) = 100 × (6.5p – 4 – 0.01p)  multiply both sides by 100

⇔ 100 × (2.3p – 10.1) = 100 × (6.5p – 4 – 0.01p)

⇔ 230p – 1010 = 650p – 400 – p

……………………………………………………

Necesito la solución.

Answers

I need the solution, I think

simplify (–2 – c )(–1)

Answers

The simplified expression of (-2 - c)(-1) is 2 + c

How to simplify the expression?

We have:

(-2 - c)(-1)

Express as product

(-2 - c) * (-1)

Evaluate the product

2 + c

Hence, the simplified expression of (-2 - c)(-1) is 2 + c

Read more about expressions at:

https://brainly.com/question/723406

#SPJ1

I dare u to solve this!​

Answers

Answer:

? = 26

Step-by-step explanation:

Challenge accepted!

For the bottom left corner:

[tex]10^{2} + 6^{2} \\= 100 + 36\\= 136[/tex]

Now, 10 - 6 = 4

136 / 4 = 34

For the top left corner:

[tex]7^{2} + 5^{2} \\= 49 + 25\\= 74[/tex]

Now, 7 - 5 = 2

74 / 2 = 37

For the top right corner:

[tex]8^{2} + 4^{2} \\= 64 + 16\\= 80[/tex]

Now, 8 - 4 = 4

80 / 4 = 20

For the bottom right corner:

[tex]6^{2} + 4^{2} \\= 36 + 16\\= 52[/tex]

Now, 6 - 4 = 2

52 / 2 = 26

Another method:

5×6+7=37

7×6-5=37

6×4+10=34

10×4-6=34

4×3+8=20

8×3-4=20

So, 4×5+6=26

6×5-4=26

Firstly we have to multiply number with smaller number from the both number, then, multiply that constant number with larger number and then subtract smaller number you will get same number, in this with 4 only 5 constant number following this rule 4×5+6=26, 6×5-4=26, if you multiply 4 with 6, then, 4×6+6=30, 6×6-4=32, and with 7, 4×7+6=34, 6×7-4=38. So, 26 is the right answer of this question

Which graph represents the function of f(x) = 4x^2-16/2x-4 ?

Answers

See the graph in the image.

y = (4x² - 16)/(2x - 4)y = [4(x-2)(x+2)]/[2(x-2)]y = 2(x+2), with a domain of all real numbers other than 2

function is a relationship between inputs where each input is related to exactly one output.

The graph of f(x) = (4x² - 16) / (2x - 4) is given below.

What is a function?

function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Function:

f(x) = (4x² - 16) / (2x - 4)

This can be written as,

f(x) = (2x)² - 4² / (2x - 4)       [ a² - b² = (a + b)(a - b) ]

f(x) = (2x - 4)(2x + 4) / (2x - 4)

f(x) = 2x + 4

Now,

We will find the coordinates from the function f(x) = 2x + 4

x = 0, f(x) = 4

(0, 4)

x = 1, f(x) = 6

(1, 6)

x = 3, f(x) = 10

(3, 10)

And so on.....

The graph is given below,

Thus,

The graph of f(x) = (4x² - 16) / (2x - 4) is given below.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ2

A,B and C are points in the cartesian plane. the coordinates of A are (3,-2),BA=(4,-3)and AC=(4,9). Calculate
i. the coordinates of B and C​

Answers

If BA and AC are vectors then AB= (-4 3)
Then B is at (3 - 4, -2 + 3) = (-1, 1)
and C is at (3 + 4, -2 + 9) = (7, 7)

If the degree of a polynomial function is even and the leading coefficient is negative, then the end behavior of the function is?

Answers

Answer:

Its the last option.

Step-by-step explanation:

The function will  rise from the left and descend to the right.

f(x) ---> -∝ as x ---> -∝ and f(x) ---> -∝ as x ---> ∝

Yaqub, Angus and Iris share 18 slices of pizza in the ratio
1:3:2.
How many slices of pizza does Iris have?

Answers

Answer:

6 Slices

Step-by-step explanation:

Total units = 1 + 3 + 2 = 6 Units

6 Units = 18 Slices of Pizza

Iris shared 2 units.

1 Unit = 18/6 = 3 Slices of Pizza

2 Units = 2 * 3 = 6 Slices of Pizza

Other Questions
the table shows the length of time in hours ,some children spent watching tv last week which of the following is NOT a type of scientist?A. GeologistB. MeteorologistC. BotanistD. Cryptologist Which statement best compares the structure of "Harlem"* and The Weary Blues"? "Harlem" is short and happy, while The Weary Blues" is longer and Iyrical. "Harlem" is short andurgent, while "The Weary Blues" iS longer and lyrical. "Harlem" iS short and content, while "The Weary Blues" is longer and unhappy."Harlem" is short and curious, while "The Weary Blues" is longer and unhappy. St^2 e^-10t dtEvaluate the intergral Given the function h of x equals negative 5 times the square root of x, which statement is true about h(x)? The function is decreasing on the interval (, 0). The function is increasing on the interval (, 0). The function is decreasing on the interval (0, ). The function is increasing on the interval (0, ). 1. Use a real-life example to describe the following allocation methods. Hint: Use family, friends, teams, church, and/or clubs for examples.Brute ForceMarketQueuingRandom SelectionTraditionEqual SharesNeedPlanned Question 11 ptsThese warriors established a colonial empire for Spain, but theydestroyed civilizations in the Americas in the process. Who were they? How do ocean currents affect temperature? Check all that apply.They carry cold water from the poles to the equator and cool air over land.They flow north and then south below the equator.They flow south and then north above the equator.They move warm water from the equator to the poles and heat air over land.They move east to west and create prevailing winds.They move west to east and create seasonal winds.PLS HELLLLPPPP MEH I HAVE BEEN ON THIS QUESTION FOR TWO WHOLE DAYS An object has a mass of 8.0 kilograms. a 2.0-newton force moves the object a distance of 3.0 meters to the east, and then 4.0 meters to the north. what is the total work done on the object Casework refers to Select one: a. appropriations that legislators secure for projects benefiting their home state or district. b. efforts by legislators to provide personal services to constituents, such as help dealing with the bureaucracy. c. direct services and benefits legislators provide to their constituents, such as appointments to offices. d. the use of free mail by legislators to keep constituents informed of governmental business and public affairs. If a firm has positive results from market testing, the next step will be the: Mi padre es plomero y mi madre es _________ profesora famosa. Which definite or indefinite article should I use if any. Match each box plot to the data set it represents.Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.{20,18,8,18,10,8,4} {12,14,16,20,4,8,10} {12,16,4,20,8,6,8} Read this excerpt from Kinnell's poem "Vapor Trail Reflected in the Frog Pond":And I hear,coming over the hills, America singing,her varied carols I hear:crack of deputies' rifles practicing their aim on stray dogsat night,sput of cattleprod,TV going on about the smells of the human body,curses of the soldier as he poisons, burns, grinds, andstabsthe rice of the world,with open mouth, crying strong, hysterical curses.What is this part of the poem about?A. America's involvement in the warB. Tadpoles who may never grow into frogsC. The rice paddies that soldiers trudge throughD. The casualties in Vietnam A survey was given to ask a group of adults if they liked chocolate or vanilla ice cream more. The table shows the survey results of three age groups.(see attachment for table)A person is selected at random. Determine the probability of each described event. Round your answers to two decimal places.P(20s | Chocolate) = ________P(Chocolate | 30s) * P(Vanilla | 30s) = ________ Identify if phosphorous is paramagnetic or diamagnetic and explain why. Mitochondria and chloroplastshave their own DNA but noorganelles.Mitochondria and chloroplasts are MOST SIMILAR to which type of cell?A. root cellsb amoeboid cellsC. prokaryotic cells Dion is reading a short story that refers to several folktales. He wants to understand the influence of this familiarmaterial on the short story.Which type of context should he consider to better understand this story?O A. MediumB. Literary traditionC. PlagiarismD. Citations Which device allows users to directly hear data from a computer How many nouns are there in the following sentence?The monarch is a kind of butterfly that migrates.