Suppose I have an urn with 9 balls: 4 green, 3 yellow and 2 white ones. I draw a ball from the urn repeatedly with replacement. (a) Suppose I draw n times. Let X., be the number of times I saw a green ball followed by a yellow ball. Calculate the expectation Ex, (b) Let y be the number of times I drew a green ball before the first white draw. Calculate E[Y]. Can you give an intuitive explanation for your answer

Answers

Answer 1

Answer:

[tex]E(X_n)=\frac{2(n-1)}{27}[/tex]

[tex]E(y)=\frac{14}{9}[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size n=9

Number of Green [tex]g=4[/tex]

Number of yellow [tex]y=4[/tex]

Number of white [tex]w=4[/tex]

Probability of Green Followed by yellow P(GY) ball

 [tex]P(GY)=\frac{4}{9}*\frac{3}{9}[/tex]

 [tex]P(GY)=\frac{4}{27}[/tex]

Generally the equations for when n is even is mathematically given by

 [tex]Probability of success P(S)=\frac{4}{27}[/tex]

 [tex]Probability of Failure P(F)=\frac{27-4}{27}[/tex]

 [tex]Probability of Failure P(F)=\frac{23}{27}[/tex]

Therefore

 [tex]E(X_n)=\frac{n}{2}*P[/tex]

 [tex]E(X_n)=\frac{n}{2}*\frac{4}{27}[/tex]

 [tex]E(X_n)=\frac{2n}{27}[/tex]

Generally the equations for when n is odd is mathematically given by

 [tex]\frac{n-1}{2}[/tex]

 [tex]E(X_n)=\frac{n-1}{2}*\frac{4}{27}[/tex]

 [tex]E(X_n)=\frac{2(n-1)}{27}[/tex]

b)

Probability of drawing white ball

 [tex]P(w)=\frac{2}{9}[/tex]

Therefore

 [tex]E(w)=\frac{1}{p}[/tex]

 [tex]E(w)=\frac{1}{\frac{2}{9}}[/tex]

 [tex]E(w)=\frac{9}{2}[/tex]

Therefore

 [tex]E(y)=[E(w)-1]\frac{4}{9}[/tex]

 [tex]E(y)=[\frac{9}{2}-1]\frac{4}{9}[/tex]

 [tex]E(y)=\frac{14}{9}[/tex]


Related Questions

plz help I really don’t understand this

Answers

Answer:

[tex]OP=3.6[/tex]

Step-by-step explanation:

Since OP is parallel to LM, the two triangles are similar, because they share all three angles. By definition, the corresponding sides of a similar polygon must be in a constant proportion.

Thus, we have:

[tex]\frac{6}{6+4}=\frac{OP}{6},\\10\cdot OP=36,\\OP=\frac{36}{10}=\boxed{3.6}[/tex]

what is the solution to the system of equations

Answers

Answer:

O  A. [tex](-1,2)[/tex]

Step-by-step explanation:

[tex]y=x+3[/tex]

[tex]2=-1+3[/tex]

[tex]2=2[/tex]

[tex]y=-x+1[/tex]

[tex]2=-1+1[/tex]            Since two -x's are being used, x becomes positive!

2 = 1 + 1

2 = 2

Solution: (-1, 2)

BRAINLIEST IF CORRECT

Generating random samples.

Answers

Answer:

1st and 3rd answer

Step-by-step explanation:

1st answer - Having a sample that is not random does not allow you to generalize the results of the experiment/study to the population because it is not representative of the population in the first place.

3rd answer - The definition of a random sample is that each member of the population has an equal chance of being selected.

Nine split into four groups is two, with a ___ of one.

Answers

Nine split into four groups is two, with a remainder of one.

Use the question below to answer the conditional probability question.

Answers

The answer should be 75/100

Explanation: there are a total of 100 employees so that is the denominator. And we are trying to find the probability of people who are married and/or have a child. We know that 75 are married and 57 have at least one child meaning 57 out of the 75 have a child. So 75 is the numerator bc it accounts for those who are married and have a child. Hope that helps!

Find the volume of the cone.
Either enter an exact answer in terms of π or use 3.14 for π

Answers

Answer:

volume of a cone formula = V=πr²h/

3

V=3.14(5)²3/3

V≈78.54

A square has the same perimeter as a triangle. The triangle's area is 16 root 3. What is the hypotenuse of the square?

Answers

Answer:

12\sqrt{2}

Step-by-step explanation:

To get the hypotenuse, first we need to get the side length of the square

Area of the square = L²

16\sqrt{3} = L²

L = 4×3

L = 12

Using pythagiras theorem to get the hypotenuse

Hyp² = 12²+12²

Hyp² = 144+144

Hyp² = 288

Hyp = \sqrt {288}

Hyp = 12\sqrt{2}

Hence the hypotenuse of the square is 12\sqrt{2}

how much square units of 50 units

Answers

Answer:

7.07106781187

Step-by-step explanation:

if its just asking [tex]\sqrt50[/tex]

:D

please help!!!!!!!!!!!

Answers

Q(1,5) R(3,-1) S(0,0) T(-2,3)

Answer:

Q(1,5)

R(3,-1)

S(0,0)

T(-2,3)

Please give brainiest?

pls help with both of them
will give brainliest and everything​

Answers

Volume of cylinder is π r^2h
So π (1.3)^2(4.83)
Why 1.3 but not 2.6 though? Because 2.6 is the diameter, to find the radius, divide the diameter by 2, so 1.3.
And so the volume of the cylinder is 29.74083in^3 or 29.74in^3 rounded to the nearest hundredth.
The volume for a triangular prism is
(bh/2)h, or (base•height/2)height.
So to find the base, take the length and width and times it.
3 1/2•1=3 1/2
The base is 3 1/2, or 3.5 inches. The height is given as 4 inches.
(3.5•4/2)4=28
The volume of the triangular prism is 28 in^3

Solve for x.

5(x – 10) = 30 – 15x

Answers

Answer:

x=4

Step-by-step explanation:

[tex]\sf 5(x - 10) = 30 - 15x[/tex]

[tex]\sf 5x-50=30-15x[/tex]

[tex]\sf 5x-50+50=30-15x+50[/tex]

[tex]\sf 5x=-15x+80[/tex]

[tex]\sf 5x+15x=-15x+80+15x[/tex]

[tex]\sf 20x=80[/tex]

[tex]\sf \frac{20x}{20}=\frac{80}{20}[/tex]

[tex]\sf x=4[/tex]

Can anyone help with this?

Answers

The pints should be a line that passes throughout (-2,1) and (0,0)

hey there, please help me. thank you

Answers

Answer:

S.S.S

Step-by-step explanation:

When three sides of a triangle are respectively equal to three corresponding sides of another triangle, they are said to be congruent .

hope it is helpful to you

a bucket contains 3 1/2 gallon of water. If Marie adds 5 gallons more, how many gallons of water will there be in all?​

Answers

Answer:

8 1/2

because 3 + 5= 8+ 1/2= 8 1/2

Express y in terms of x

Answers

Answer:

see explanation

Step-by-step explanation:

(a)

Given y is inversely proportional to x² then the equation relating them is

y = [tex]\frac{k\\}{x^2}[/tex] ← k is the constant of variation

To find k use any ordered pair from the table.

Using (1, 4 ) , then

4 = [tex]\frac{k}{1^2}[/tex] = [tex]\frac{k}{1}[/tex] ( multiply both sides by 1

4 = k

y = [tex]\frac{4}{x^2}[/tex] ← equation of variation

(b)

When y = 25 , then

25 = [tex]\frac{4}{x^2}[/tex] ( multiply both sides by x² )

25x² = 4 ( divide both sides by 25 )

x² = [tex]\frac{4}{25}[/tex] ( take the square root of both sides )

x = ± [tex]\sqrt{\frac{4}{25} }[/tex] = ± [tex]\frac{2}{5}[/tex]

Since x > 0 then x = [tex]\frac{2}{5}[/tex]

can someone help me understand this, please? For some reason my answer is correct but I need to understand how did I found the correct answer

Answers

Answer with step-by-step explanation:

The way the question is worded, this actually shouldn't be correct. The correct answer should be [tex]3:4[/tex].

Because the trapezoids are similar, we can find the ratio of their perimeters by actually just finding the ratio of their sides.

Why?

By definition, the corresponding sides of a polygon are in a constant proportion. The perimeter is simply the sum of all sides of the polygon. Since we're just adding the sides, the proportion will still be maintained.

Therefore, we'll just need to ratio of their corresponding sides. The only two corresponding sides that are marked are [tex]\overline{RS}[/tex] and [tex]\overline{AB}[/tex].

The ratio of [tex]\overline{RS}:\overline{AB}[/tex] is [tex]18:24\implies \boxed{3:4}[/tex].

The reason why it ideally should be [tex]3:4[/tex] and not [tex]4:3[/tex] is because the question states [tex]RTSU\sim ABCD[/tex], which mentions [tex]RSTU[/tex] first, so our answer should follow this respective order. I believe you were marked right anyways because the specific order is not specified, but generally, you want to give your answer respectively by default.

Andrea played dominos nonstop for 52 minutes in Little Havana. If each match lasted 13 minutes, how many matches did she play in that time?

Answers

Answer:

4 Matches

Step-by-step explanation:

According To the Question,

Given, Andrea played dominos nonstop for 52 minutes.And, each match lasted 13 minutes .

Now, The Total Matches she plays in that time = [tex]\frac{(Total Time Played)}{(Time On Each Match)}[/tex]

Thus, Total Matches = 52 / 13 ⇔ 4 Matches

URGENT PLZ HELP: Graph y = tanx for -pi/4 ≤ x ≤ x/4.
What is the range?

Answers

I believe that the answer is D) all real numbers.

solve it : -

[tex] \sqrt{6 \times 24} [/tex]
_______​

Answers

Answer:

12

Step-by-step explanation:

sqrt(6*24)

sqrt(144)

sqrt(12*12)

12

Answer:

12

Step-by-step explanation:

6×24=144

Sq. Root of 144=12

х
4
16
Find the exact value of x.
=

Answers

Answer:

The value of x is 8

Step-by-step explanation:

 

Mike works h hours in a week. To find his weekly pay he multiplies his hours by his pay of $30 per hour and adds $5 for his sales bonus. He's decided that he wanted to take one-fifth of his weekly pay and place it in his savings. Which simplified expression represents the amount that will go into his savings each week?

Answers

Answer:

6h + 1

Step-by-step explanation:

number of hours: h

pay per hour: 30

pay for the hours: 30h

add sales bonus: 30h + 5

1/5 of total above: (1/5)(30h + 5) = 6h + 1

Answer: 6h + 1

If someone were to have 300 feet of fencing, what is the maximum area they can enclose?

Answers

Answer:

I think it would be 5,625ft^2?

Step-by-step explanation:

300÷4=75

75×75=5,625

Which is the graph of the linear inequality 1/2x - 2y > -6?

Answers

Answer: almost there

Step-by-step explanation: bring the 2 up

602.88 rounded to 2 decimal place is ?​

Answers

Answer:

it will be 603.00

it will. e counted from the right to the left

To solve for the missing length, which operation should you perform?

Answers

Answer:

? = 15 yards

Step-by-step explanation:

h² + b² = ?²

9² + 12² = ?²

81 + 144

225

√225 = 15

Answer:

Pythagorean theorem

Step-by-step explanation:

You should use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

9^2+ 12^2 = ?^2

81 +144 = ?^2

225 = ?^2

Take the square root of each side

sqrt(225) = sqrt(?^2)

15 =?

In, z = 4 cm, x=8cm, and m

Answers

Answer:

what do u want us to do pls be more clear!

A is the point with coordinates (x, 2y).
B is the point with coordinates (3x, 4y).
The midpoint of AB has coordinates (-4, 15).
Work out the values of x and y.​

Answers

Answer:

x= -2 , y=5

Step-by-step explanation:

(x+3x)/2 = -4

4x/2 = -4

4x= -8

x = -2

(2y+4y)/2=15

6y/2=15

6y=30

y=5

What additional information is needed to prove the triangles congruent by SSS

Answers

Answer:

Angle a = Angle D

Answer:

A: Angle A  Angle D

Step-by-step explanation:

work out the average speed of 40 km in 2.5 hours​

Answers

Answer:

19.20

Step-by-step explanation: used

a calc

Pls help if you only know the correct answer! Thanks! :)

Answers

Answer:

A. -3/5 B. 1/5. C. 0.8.

Step-by-step explanation:

Since A is on the left side of 0, it will be negative, in which -3/5 is the only negative answer on there, so A= -3/5. Since B is on the right side of the 0 it's positive, and it is equal to 1/5 which gets you to 0.20, which will be the value of each line since 1 divided by 5 is equal to 0.20. 0.8 is also known as 0.80 so C will be next to the 1.

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