An urn contains b black balls and r red balls. One of the balls is drawn at random, but when it is put back in the urn c additional balls of the same color are put in with it. Now suppose that we draw another ball.

Required:
Show that the probability that the first ball drawn was black given that the second ball drawn was red is b/(b r c).

Answers

Answer 1

Answer:

Please see the explanation below for proof

Step-by-step explanation:

Probability of choosing black ball from the bag

[tex]\frac{b}{b+r}[/tex]

Probability of choosing red ball from the bag

[tex]\frac{r}{b+r}[/tex]

After the addition of c balls of correspondent color –  

P (R2/B1) [tex]= \frac{r}{(r+b+c)}[/tex]

P (R2/B2) [tex]=\frac{r+c}{(r+b+c)}[/tex]

B1 and B2 are mutually exclusive event

P (B1/R2) = [tex]\frac{\frac{r}{(r+b+c)} *\frac{b}{b+r}}{\frac{r}{(r+b+c)}*\frac{b}{b+r} + \frac{r+c}{(r+b+c)}* \frac{b}{b+r}}[/tex]

P (B1/R2) [tex]=\frac{b}{(r+b+c)}[/tex]

Hence, Proved


Related Questions

Please help!!!!

If f(1) = 2 and f(n+1) = f(n)^2 – 3 then find the value of f(3).

Answers

Answer:

The value of f(3) is -2.

Step-by-step explanation:

This is a recursive function. So

[tex]f(1) = 2[/tex]

Now, we find f(2) in function of f(1). So

[tex]f(1+1) = f(1)^2 - 3[/tex]

[tex]f(2) = f(1)^2 - 3 = 2^2 - 3 = 1[/tex]

Now, with f(2), we can find the value of f(3).

[tex]f(2+1) = f(2)^2 - 3[/tex]

[tex]f(3) = f(2)^2 - 3 = 1^2 - 3 = -2[/tex]

The value of f(3) is -2.

Hal earns n dollars per hour. Next month he
will receive a 296 raise in pay per hour. The
expression n +0.02n is one way to represent
Hal's pay per hour after the raise Write an
equivalent simplified expression that will
represent his pay per hour after the raise.

Answers

Answer:

[tex]Total = 1.02n[/tex]

Step-by-step explanation:

Given

[tex]Earnings = n[/tex]

[tex]Raise = 2\%[/tex] --- not 296

[tex]Total = n + 0.02n[/tex]

Required

Simplify the expression for total earning

The total amount is derived from:

[tex]Total = Earnings + Raise * Earnings[/tex]

[tex]Total = n + 2\% * n[/tex]

Express percentage as decimal

[tex]Total = n + 0.02 * n[/tex]

Now, we can solve further:

[tex]Total = n + 0.02n[/tex]

[tex]Total = 1.02n[/tex]

Hence, the simplified expression is 1.02n

Answer:

1.02n

Step-by-step explanation:

−3.64⋅|−5.3|−1.5^3

help pls

Answers

Answer:

5

Step-by-step explanation:

its 45

Answer:

-22.667

Step-by-step explanation:

-3.64(5.3) - (1.5)³

-19.292 - 3.375 = -22.667

Candice is preparing for her final exam in Statistics. She knows she needs an 62 out of 100 to earn an A overall in the course. Her instructor provided the following information to the students. On the final, 200 students have taken it with a mean score of 54 and a standard deviation of 6. Assume the distribution of scores is bell-shaped. Calculate to see if a score of 62 is within one standard deviation of the mean.

Answers

Answer:

A score of 62 is not within one standard deviation of the mean.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mean score of 54 and a standard deviation of 6.

This means that [tex]\mu = 54, \sigma = 6[/tex]

Calculate to see if a score of 62 is within one standard deviation of the mean.

Is Z between -1 and 1 when X = 62?

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{62 - 54}{6}[/tex]

[tex]Z = 1.33[/tex]

So a score of 62 is not within one standard deviation of the mean.

A rectangle is 4 times as long as it is wide. The perimeter is 30 feet. Find the dimensions.

Answers

Answer:

Express your length and width as algebraic expressions:

 

width = x

length = 4x

 

Use the formula for the perimeter of a rectangle to solve for x:

 

perimeter = 2(length) + 2(width)

50 = 2(4x) + 2(x)

50 = 8x + 2x

50 = 10x

5 = x

 

The width (x) is 5 feet and the length (4x) is 20 feet.

Step-by-step explanation:

Answer: 3 by 3 by 12 by 12

Step-by-step explanation: Two sides are x feet long. The two other sides are 4 times x feet long. 4x+4x+x+x =10x

Set that equal to 30 and solve. x=3

Plug back into the original 4x's and x's to get the lengths

Which of the following is NOT type of magnet

a
permanent magnet
b
electromagnet
c
temporary magnet
d
Domain magnet

Answers

Answer:

Is not a type of magnet a domain magnet

Choose the smallest number.

0.03
0.3003
O 0.009
0.093
1.0001

Answers

Answer:

0.009

Step-by-step explanation:

We can figure this one out by looking at first the ones place to see if it's a zero, then the tenths and hundredths place, checking if those are also zeros. Because this is the only number with those three numbers as zeros, it is the smallest.

The answer is 0.009
This is because you must look at where the zeros are and how much zeros are there

Hurry I am timed Which tiny, round “factory” puts together protein and is often found in the endoplasmic reticulum?


ribosome


chromosome


Golgi body


chloroplast

Answers

Answer:

the answer is ribsome

The ribosome serves as the site and carries the enzymes necessary for protein synthesis. They are often takes the shape of small round particles attached in the endoplasmic reticulum.

Which geometric sequence has a common ratio of -9?
{-1, -9, 81, 729, …}
{1, -9, 81, -729, …}
{-9; -81; -729; -6,561; …}
{81; 729; 6,561; 59,049; …}

WILL GIVE BRAINLIEST!!!!

Answers

Answer:

second one

Step-by-step explanation:

just multiply by -9 and see which one fits in

Answer:

{1, -9, 81, -729, …}

Step-by-step explanation:

Geometric sequence is basically multiplying the previous number by the constant. So it is 1 x -9 = -9, -9 x -9 = 81, -81 x -9 = -729, and so on.

Identify the coordinates for point D​

Answers

Answer:

Your Picture is just of -3????

Step-by-step explanation:

Once sales tax is included, a $62 hammock ends up costing $67.58. What is the sales
tax percentage?
NEED ASAP WILL GIVE BRAINLIEST

Answers

Answer:

9%

Step-by-step explanation:

subtract 62 from 67.58 to get 67.58-62=5.58divide 62 by 5.58and your final answer is 9%

Pls help periodddd pooh

Answers

Answer:

the answer is n = -7

I also put a image to show you how to solve the equation. I hope the image helps.

Answer:

n= -7

Step-by-step explanation:

function not a function ?

Answers

Answer:

not a function

Step-by-step explanation:

Pls answer allllll! I really need it

Answers

Answer:

7) I believe it is "The sum of the large rectangle is equal to the sum of the two smaller rectangles. 3 (x + 4)" But I am not sure.

8) Make it shorter and simpler by combining like terms

9) 5x , 2a + 3 + a + 4 , 6 + 2x + x2 + 1 + x

10) ac + bc = (a + b) c

Step-by-step explanation:

In a shop, a TV has a normal price of £500
The shop has a sale.

On Monday, the normal price of the TV is reduced by 1/10 to give the sale price.
On Tuesday, the sale price of the TV is reduced by 20%

Chris wants to buy the TV.
He has £400 to spend on the TV.

Does Chris have enough money to buy the TV on Tuesday?

Answers

Answer:

400> 360

Step-by-step explanation:

1/10 X 500 = 50

500 - 50 = 450

10% = 450/ 10 = 45

20% = 45 x 2 = 90

450 - 90 = 360

Chris does have enough 400> 360

An array of 30 LED bulbs is used in an automotive light. The probability that a bulb is defective is 0.001 and defective bulbs occur independently. Determine the following: a. Probability that an automotive light has two or more defective bulbs. b. Expected number of automotive lights to check to obtain one with two or more defective bulbs.

Answers

Answer:

a) 0.0005 = 0.05% probability that an automotive light has two or more defective bulbs.

b) 4000 automotive lights.

Step-by-step explanation:

For each LED, there are only two possible outcomes. Either it is defective, or it is not. Defective bulbs occur independently, which means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

An array of 30 LED bulbs is used in an automotive light. The probability that a bulb is defective is 0.001.

This means that, respectively, [tex]n = 30, p = 0.001[/tex].

a. Probability that an automotive light has two or more defective bulbs.

This is:

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{30,0}.(0.001)^{0}.(0.999)^{30} = 0.9704[/tex]

[tex]P(X = 1) = C_{30,1}.(0.001)^{1}.(0.999)^{29} = 0.0291[/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.9704 + 0.0291 = 0.9995[/tex]

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.9995 = 0.0005[/tex]

0.0005 = 0.05% probability that an automotive light has two or more defective bulbs.

b. Expected number of automotive lights to check to obtain one with two or more defective bulbs.

0.0005 = 0.05% probability that an automotive light has two or more defective bulbs.

The number of expected trials to obtain n successes with p probability is given by:

[tex]E = \frac{n}{p}[/tex]

In this case, we have that [tex]n = 2, p = 0.0005[/tex]. So

[tex]E = \frac{n}{p} = \frac{2}{0.0005} = 4000[/tex]

4000 automotive lights.

Select the numbers that have a factor of 5. Mark all that apply.
D
2
A 15
5
3.
(В)
E
50
(F) 31
© 45

Answers

Answer:

a number ending in 0 or 5 has a factor of 5

Step-by-step explanation:

5 is a factor of

5, 10, 15, 20, 25...

any number that ends in 0 or 5 would qualify

Simplify the inequalities and match them with the graphs that represent them. 7x < 42 3x >15 2x > 12 X + 1 < 8 T G DEL ਨੂੰ ਜਨ : ' ! 2 ! ! T } ts reserved​

Answers

Answer:

14 times pie = 69

Step-by-step explanation:

Decrease £14120 by 4% Give your answer rounded to 2 DP.

Answers

Answer:

(14120/100)*96 = £13,555.20

Step-by-step explanation:

Answer:

£13,555.20

Step-by-step explanation:

14120*4=56480

56480+14120=70,600

then 70,600+20

on a cauculaiter it will give you 70,620 but it is 70,600.20

then 14,1000.50-1,555.30=13,55.20

hope it is helpfull

5 × ( 1 / 3 + 2 / 5 ) =

write your answer as a mixed number

Answers

Answer: the answer is 2 and 1/15

Step-by-step explanation:

78 - 24 : (14 - 6) X 2

Answers

Answer:

ehfrbff rf rh g5e

Step-by-step explanation:

fnebghrbgy5gty5hfegwrnfybgrvthr4yftbgryibr4th45f94ny7rfjhyrjfrhvgruf

Answer:

3 3/8 or 3.375

Step-by-step explanation:

simplify

54:8x2

54/16

3 3/8

i need help please and thank you

Answers

Answer:

F- the first answer choice

Step-by-step explanation:

Answer:

answer is h

Step-by-step explanation:

a is at -3 1/2, 3 1/2 b is at 5, -2 1/2

what 30 x 23 30 x 23

Answers

30 x 23 = 690

23 x 30 = 690

Answer: 690

Step-by-step explanation:

Now whats 34+35?

Which statement must be true according to the dot plot?

The data is skewed to the right and shows that she never scored fewer than 2 points or more than 12 points in a game.
The data is skewed to the right and shows that she scored 11 points in more games than all of the other games combined.
The data is skewed to the left and shows that she never scored fewer than 2 points or more than 12 points in a game.
The data is skewed to the left and shows that she scored 11 points in more games than all of the other games combined.

Answers

Answer: c

Step-by-step explanation:

just did on edg :) got a 100%

Answer:

c

Step-by-step explanation:

Grace and her friend are doing some back to school shopping , Grace buys 4 binders and notebooks for 26.50 totalHer friend spends a total of $21.00 on 3 binders and 6 notebooks

Answers

Answer:

What is the question asking to answer?

Step-by-step explanation:

Answer:

$19:50

Step-by-step explanation:

Write a system of equations to represent the problem. Let x represent the cost of a binder, and let y represent the cost of a notebook.

Grace buys 4 binders and 7 notebooks for $26.50 total, so the equation 4x+7y=26.50 represents how much Grace spends.

Grace's friend buys 3 binders and 6 notebooks for $21.00 total, so the equation 3x+6y=21 represents how much her friend spends.

You can use this system of equations to find how much money Grace and her friend spend on notebooks:

4x+7y=26.50

3x+6y=21

Next, find how much Grace and her friend spent on notebooks. Start by finding the cost of one notebook. Use elimination to solve for y. .

3(4x+7y)=3(26.50)  

12x+21y = 79.50

4(3x+6y)=

4(21)  

12x–24y =  

84

3y =  

4.50

y = 1.50

Each notebook costs $1.50. Grace and her friend buy a total of 13 notebooks, so multiply to find how much money they spend on notebooks.

13$1.50=$19.50

Grace and her friend spend $19.50 total on notebooks.

Hamdan scored 8 out of 10 on his history quiz. Which is his score as a fraction in simplest form?
2 over 5
4 over 5
6 over 10

Answers

Answer:

4 over 5

Step-by-step explanation:

The simplist form of 8/10 is 4/5.

Answer: 8/10 is a 4/5

Step-by-step explanation:

Which set of angles will be complimentary

Answers

∠1 + ∠3 + 90° = 180°

∠1 + ∠3 = 90°

∠3 = ∠4 (vertically opposite angles)

∠1 + ∠4 = 90°

Therefore, the answer is ∠1 + ∠4

(t−6)^2 t = 11 What is the answer please.

Answers

Answer:

25

Step-by-step explanation:

t = 11, so let's put 11 in place of t in the equation.

(11-6)^2

PEMDAS tells us parenthesis first, so let's do that.

(5)^2

Now let's square it.

5*5=25

So there you go, 25 is your answer :)

The line plot above shows the height of the baby giraffes at the zoo. What is the difference in height (in inches) between the shortest and the tallest baby giraffes?​

Answers

Answer:

3.5 inches

Step-by-step explanation:

Height of tallest baby giraffe = 42.75 inches

Height of shortest baby giraffe = 39.25 inches

Difference in height between the tallest and the shortest baby giraffes = 42.75 - 39.25 = 3.5 inches

What are expressions that are equivalent to -4/3p - 2/5?

Answers

-4/3 - 2/5

HOPE THAT HELPS DUDE

Other Questions
Please help thank you What does the pattern in the image above represent?OA. the phases of the MoonOB. the patterns of the starsOC. the seasons of the yearOD. the cycle of the Sun Why is it important to be prepared before any harm In what way did the physical geography of northern Europe affect the ethnic diversity of the region?A) A lack of significant physical barriers allowed for easy migration to the area.B) Extremely cold climate conditions made it difficult to live in the region.C) Vast waterways across the plains blocked the flow of migrants.D) Multiple mountain ranges acted as a barrier to cultural convergence. Based on the triangles, Which statement about x is true? In which of the following regions does most of the commercial agriculture in the United States take place? Will mark Brainliest!!!! the three are perpendicularparallel neither parallel nor perpendicular Solve expression completely.4-3O 1/64O-64O 1/16O64 Find the slopes form two points (1, -2) and (3,-4) Decide whether each statement on the right is a fact, an opinion, or a combination of the two. Match each to thephrase that describes it.opinion, supported by factFrida Kahlo was bold, I believe, whenshe brought her art to Diego Rivera.fact onlyFrida Kahlo was in a bad bus crashfact, along with opinionI think Frida Kahlo was lonely.opinion onlyDiego Rivera painted Frida Kahlo. Hemust have liked her a lot. which is a good way to create wealth?a: buying a homeb: buying a used carc: renting an apartment Four people are pulling in different directions on a shopping cart. The magnitude of their pulling forces and the directions relative to straight east are indicated below. Jane: 80 pounds, straight east (0 degrees relative to east) Brittany: 100 pounds, north (90 degrees relative to east) Robyn: 80 pounds, southwest (225 degrees relative to east) Scott: 100 pounds, northwest (135 degrees relative to east) Which way with the shopping cart go? Read the sentence.As the boy sneaked down the hallway, he came upon a door that was ajar, which he could just barely peek through to see the splendid artifacts displayed in their carefully locked cases.The definition of ajar is slightly open. Which context clue confirms this meaning?A. Ajar is a synonym of door.B. Ajar is an adverb describing the boy.C. Ajar is an adjective describing the door.D. Ajar is a noun referring to the artifacts. Which of the following is a function? Refer to the article From Barter to Bitcoin in your Money, Money, Money magazine for a complete version of this text.Based on the information in From Barter to Bitcoin, one can conclude that when it became inefficient to fulfill their needs and wants through trade, people began using currency.Which detail from the text best supports this conclusion?A. As cities blossomed and farming progressed, the barter economy no longer worked so well.B. People started growing crops and raising animals such as goats and pigs.C. The original currency was probably a measure of grain, such as a bushel of wheat or barley.D. The toolmaker can then use that money to buy new boots directly from the shoemaker. can somebody help me The manager of a supermarket records the waiting times of 100 customers.He wishes to calculate an estimate for the mean waiting time.He draws this table.Waiting TimeNumber ofMidpoint (x)fx(minutes)customers (0)0-0.552.51 -1.528422 -2.532803.526913-4-54.5940.5100256a) Complete the table.b) Calculate an estimate for the mean. (I JUST NEED HELP ON B) Which sentence best shows correct comma usage? Compare and contrast the AA similarity criterion with the ASA congruence criterion. Choose the correct answer.A. Both criteria require that two pairs of angles be congruent, but for congruence you also need to know that the included sides are congruent, so that the figures are the same size. The AA similarity criterion shows only that the two triangles are the same shape. B. Both criteria require that two pairs of angles be congruent, but for congruence you also need to know that the non-included sides are congruent, so that the figures are the same size. The AA similarity criterion shows only that the two triangles are the same shape.C. Both criteria require that two pairs of angles be congruent, but for congruence you also need to know that the included sides are congruent, so that the figures are the same size. The AA similarity criterion shows only that the two triangles are the same size.D. Both criteria require that two pairs of sides be congruent, but for congruence you also need to know that the included angles are congruent, so that the figures are the same size. The AA similarity criterion shows only that the two triangles are the same shape. use the information in the diagram to determine the height of the tree. the diagram is not to scale.