Two fair dice are rolled. Find the joint probability mass function of x
and y
, when x
is the largest value obtained on any die and y
is the sum of the values.

Answers

Answer 1

a) P(X = x₀, Y = 2x₀) = 1/36

P(X = x₀, Y = k) = 1/18 for k between x₀+1 and 2x₀-1 inclusive

Every other event has probability 0. x₀ is any number between 1 and 6 inclusive.

b) P(X = x₀, Y = x₀) = x₀/36

P(X = x₀, Y = k) = 1/36 for k between x₀+1 and 6 inclusive.

x₀ is between 1 and 6 inclusive. Every other event has probability 0.

c) P(X = x₀, Y = x₀) = 1/36

P(X = x₀, Y = k) = 1/18 with k between x₀+1 and 6 inclusive

x₀ between 1 and 6 inclusive. Any other event has probability 0.

What is a joint probability?

Joint probability is the probability of two events happening simultaneously.

Let P(A) = probability that event A takes place and P(B) = probability that event B takes place. Then, probability of event A and B happening together i.e. P(A and B) is called joint probability.

What is the Calculation of joint probability?

(1) When A and B are independent events: When event A has no impact on event B or vice versa, the two events are said to be independent. For independent events, formula for joint probability is:

P(A and B) = P(A) × P(B)

Example: I am performing two acts at a time (i) tossing a coin and (ii) throwing a dice. What is the probability that the coin shows up “head” and the dice shows up “3”?

There is no doubt that getting “head” on coin and getting “3” on dice are independent events.

Probability of the coin showing up “head” = 1/2

Probability of the dice showing up “3” = 1/6

Therefore, probability of getting “head” on coin and “3” on dice = (1/2)×(1/6) = 1/12

(2) When A and B are dependent events: If event A and event B cannot be considered independent, calculation of joint probability requires knowledge of conditional probability. For dependent events, formula for joint probability is:

P(A and B) = P(A) × P(B, given A) = P(B) × P(A, given B).

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Related Questions

The tenants in an apartment building voted on whether to places couches in the lobby of the building. The number of votes for placing couches in the lobby was 765. The number of votes against placing couches in the lobby was 1,785. What percent of the voters were in favor of placing couches in the lobby of the building.REEEEE
A.20%
B.25%
C.30%
D.35%

Answers

C. 30%
you just need to add 1785 and 765 which would give you 2,550. From there, I honestly just guessed 30% then figured out 30% of 2550 which is 765.

A manufacturer of band saws wants to estimate the average repair cost per month for the saws he has sold to certain industries. He cannot obtain a repair cost for each saw, but he can obtain the total amount spent for saw repairs and the number of saws owned by each industry. Thus, he decides to use cluster sampling, with each industry as a cluster. The manufacturer selects a simple random sample of n = 20 from the N = 96 industries he services. The data on total cost of repairs per industry and number of saws per industry are as given in the accompanying table. Estimate the average repair cost per saw for the past month and place a bound on the error of estimation.
Industry No.of saws Total repair cost for past month
1 3 50
2 7 110
3 11 230
4 9 140
5 2 60
6 12 280
7 14 240
8 3 45
9 5 60
10 9 230
11 8 140
12 6 130
13 3 70
14 2 50
15 1 10
16 4 60
17 12 280
18 6 150
19 5 110
20 8 120

Answers

Answer:

The average repair cost per saw for the past month is 20.

The bound of error of estimation is ±10.

Step-by-step explanation:

a) Data and Calculations:

Industry        No.of saws   Total repair cost   Average

                                           for past month

1                            3                        50           16.67

2                           7                        110           15.71

3                          11                       230          20.91

4                          9                        140           15.56

5                          2                         60           30

6                         12                       280           23.33

7                         14                       240           17.14

8                          3                         45           15

9                          5                        60           12

10                         9                      230           25.56

11                          8                       140           17.50

12                         6                       130           21.67

13                         3                        70           23.33

14                         2                        50           25

15                         1                          10           10

16                        4                         60           15

17                       12                       280           23.33

18                        6                        150           25

19                        5                         110           22

20                       8                        120           15

Total               130                    2,565           19.73

Average = Sum of the total repair cost for past month divided by the number of saws repaired

= 19.73 (2,565/130)

= 20

The bound on error of estimation = the difference between the upper bound of the interval and the calculated mean

= 30 - 20

= 10

The lower bound = 10

The bound of error is also = (30 -10)/2 = 10

PLEASE HELP!
The equation of a parabola is y=1/2x^2+6x+23.


What is the equation of the directrix?


y = 5.5


y = 4.5


​y = 2​


​y = 0.5

Answers

Answer:

Step-by-step explanation:

y = ½x² + 6x + 23

  = ½(x² + 12x) + 23

  = ½(x² + 12x + 6²) - ½(6²) + 23

  = ½(x+6)² + 5

vertex (-6,5)

focal length = 1/(4∙½) = ½

directrix: y = 5-½ = 4.5

Answer: y=4.5 Just confirming

Step-by-step explanation:

Just a test good luck

d. Cloe has 84 packs of potato chips and 86 juice boxes.
He wants to share them equally with all his friends. How
A many friend does Cloe have
? How many packs of chips
and juice boxes will each friend receive? is it LCM or GCF?​

Answers

Answer:

I was trying to look up the answer to help out but I think I accidently found the answer key ill put it in the explanation

Step-by-step explanation:

https://www.louisianabelieves.com/docs/default-source/assessment/grade-7-answer-key.pdf?sfvrsn=e005981f_2

Solve for x and show work please!

Answers

Answer:

Every quadrilateral's 4 angles add up to 360 degrees.

The four angles would be 100° + 7x +37 + 100° + 7x +37 = 360°

200° + 14x + 74° = 360°

14x = 360° - 274

14x = 86

x = 6.1428571429

Step-by-step explanation:

Answer: x=43/7

Step-by-step explanation:

One of the properties of the inner angle of a parallelogram is that the two angles on the same side add up to 180°

100+(7x+37)=180

100+7x+37=180

137+7x=180

137+7x-137=180-137

7x=43

x=43/7≈6.14

Hope this helps!! :)

Please let me know if you have any questions

How many times greater is 6,680 than 668

Answers

Answer:

10

Step-by-step explanation:

668 x 10 = 6,680

The radius of a cylindrical water tank is 4 ft, and its height is 10 ft. What is the volume of the tank?

Answers

Answer:

502 cubic feet

Step-by-step explanation:

The Volume of the tank is 502 cubic feet.

34 in.
16 in.
22 in.
Lateral Surface Area =
in squared
Total Surface Area =
in squared
Volume =
in cubed

Answers

Answer:

Step-by-step explanation:

Lateral surface area of the triangular prism = Perimeter of the triangular base × Height

By applying Pythagoras theorem in ΔABC,

AC² = AB² + BC²

(34)² = (16)² + BC²

BC = [tex]\sqrt{1156-256}[/tex]

     = [tex]\sqrt{900}[/tex]

     = 30 in.

Perimeter of the triangular base = AB + BC + AC

                                                      = 16 + 30 + 34

                                                      = 80 in

Lateral surface area = 80 × 22

                                  = 1760 in²

Total Surface area = Lateral surface area + 2(Surface area of the triangular base)

Surface area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                                                           = [tex]\frac{1}{2}(30)(16)[/tex]

                                                           = 240 in²

Total surface area = 1760 + 2(240)

                               = 1760 + 480

                               = 2240 in²

Volume = Area of the triangular base × Height

             = 240 × 20

             = 4800 in³

Un círculo tiene una circunferencia de 18.4 m. Determina el valor del radio. (Utiliza el valor de π = 3.14)

Answers

Answer: 2.92

Step-by-step explanation:

De la circunferencia del círculo, se encuentra que su radio es de 2.93m.

El circunferencia de un círculo de radio r es dada por:

[tex]C = 2\pi r = 2(3.14)r = 6.28r[/tex]

En este problema, la circunferencia es de 18.4. Así, es posible aplicar la fórmula de la cincumference para encontrar su radio, puesto que [tex]C = 18.4[/tex].

[tex]C = 6.28r[/tex]

[tex]6.28r = 18.4[/tex]

[tex]r = \frac{18.4}{6.28}[/tex]

[tex]r = 2.93[/tex]

El radio es de 2.93m.

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A survey conducted by the U.S. department of Labor found the 48 out of 500 heads of households were unemployed. Compute a 99% confidence interval for the proportion of unemployed heads of households in the population. Round to three decimal places. (make sure to type a zero in front of the decimal place ie. 0.1 vs .1 otherwise your answer will be marked incorrect) Lower limit

Answers

Answer:

99% Confidence interval is given as;

Lower Limit = 0.062

Upper Limit = 0.130

Step-by-step explanation:

Given the data in the question;

x = 48

n = 500

sample proportion p = x/n = 48/500 = 0.096

with 99% confidence

significance level ∝ = 1 - 99% = 1 - 0.99 = 0.01

∝/2 = 0.01 / 2 = 0.005

Critical Z-value = [tex]Z_{\alpha /2[/tex] = [tex]Z_{0.005[/tex]  = 2.576

Now,

Standard error of p : SE = √[ (p × ( 1 - p) / n ) ]

we substitute

SE = √[ (0.096 × ( 1 - 0.096) / 500 ) ]

SE = √[ (0.096 × 0.904) / 500  ]

SE = √[ 0.086784 / 500 ) ]

SE = 0.0131745

so

Margin of Error E = [tex]Z_{\alpha /2[/tex] × SE

E = 2.576  × 0.0131745

E = 0.0339

Now 99% confidence interval will be

⇒ 0.096 ± 0.0339

⇒ (0.096 - 0.0339, 0.096 + 0.0339 )

⇒ ( 0.062, 0.130 )

Lower Limit = 0.062

Upper Limit = 0.130

4x + y = 23
3x - y = 11

Answers

Answer:

Step-by-step explanation:

4x + y = 23

3x - y = 11

I got x = 34/7

Answer:it will be x= 34/7 and y= 25/7

Step-by-step explanation:4x+y=23for y:

4x+y=23

4x+y+−4x=23+−4x(Add -4x to both sides)

y=−4x+23

−4x+23foryin3x−y=11:

3x−y=11

3x−(−4x+23)=11

7x−23=11(Simplify both sides of the equation)

7x−23+23=11+23(Add 23 to both sides)

7x=34

7x

7

=

34

7

(Divide both sides by 7)

x=

34

7  

Step: Substitute

34

7

forxiny=−4x+23:

y=−4x+23

y=−4(

34

7

)+23

y=

25

7

(Simplify both sides of the equation)  

Answer:

x=

34

7

and y=

25

7  

Jim caught 15 fish over course of 3 days. After 4 days how many total fish will Jim have caught?

Answers

Answer:

20

Step-by-step explanation:

15 divided by 3 is 5

15 over 4 days = 20

x2 + 16x – 2 = 11
1) Rewrite the equation by completing the square.
Your equation should look like (x + c)2 = d or (x - c)2 = d.
I
+
utan
pls help

Answers

Answer:

(x+8)^2=77    and   x=negative 8±√77

Step-by-step explanation:

After watching a video, I got it right on Khan

The equation with completing the squares is (x + 8)² = 77.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

x² + 16x - 2 = 11

We can make complete squares.

x² + 16x - 2 - 11 = 0

x² + 16x - 13 = 0

x² + 2 x 8 x (x) -8² + 8² - 13 = 0

(x² + 16x + 8²) - 64 - 13 = 0

(x + 8)² - 77 = 0

(x + 8)² = 77

Thus,

The equation is (x + 8)² = 77.

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If the logarithm of 5832 is 6, what is the base?
[tex] logx(5832) = 6[/tex]

Answers

Answer:

The base is 4.2426.

Step-by-step explanation:

Logarithm definition:

Suppose we have that:

[tex]\log_{a}{b} = c[/tex]

It means that;

[tex]b = a^c[/tex]

In this question:

[tex]\log_{x}{(5832)} = 6[/tex]

It means that:

[tex]x^6 = 5832[/tex]

[tex]x = \sqrt[6]{5832}[/tex]

[tex]x = (5832)^{\frac{1}{6}}[/tex]

[tex]x = 4.2626[/tex]

The base is 4.2426.

the area of a rectangle with a height of 2 and a width of 5x^2-2x+3

Answers

Answer:

Area is 10x^2 - 4x + 6

Step-by-step explanation:

To find this area, multiply the width and height together:

(5x^2 - 2x + 3)(2) = 10x^2 - 4x + 6

Find the measurements of the numbered angles in each kite

Answers

Answer:

∠1 = 23°

∠2 = 23°

Step-by-step explanation:

Calcular el valor de la fuerza que se debe aplicar para dezlisar un bloque de la siguiente figura a velocidad constante, si tiene un peso de 150 N y al coeficiente de friccian dinamico es de 0.3​

Answers

Answer:

azsdfghjkljhgfdsasdfghjm,.

Step-by-step explanation:

If an object travels at 2 feet per second, how many feet does it travel in 3 hours?

Answers

Object will cover 21600 feet in 3 hours.

What is distance?

Distance is defined as the product of the speed and time.

The distance an object travelled is measured in distance per second here.

So, let us convert the hours into seconds to arrive at our answer.

One hour = 60 minutes = (60×60) seconds = 3600 seconds.

The object travels 2 feet for every second.

Then, total distance covered in 3 hours is

2×3×3600 = 21600 feet.

Hence, object will cover 21600 feet in 3 hours.

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Find the side length of a square with an area of 1521 m².​

Answers

Answer:

39

Step-by-step explanation:

a=A=1521=39

A small bar of gold measures 20 mm by 250 mm by 2 mm. One cubic millimeter of gold weighs about
0.0005 ounces. Find the volume in cubic millimeters and the welght in ounces of this small bar of gold.
cubic millimeters and the weight of the bar is
The volume of the bar is
ounce(s).

Answers

Answer: 5 ounces

Step-by-step explanation:

volume is 20*250*2=10000 cubic mm

10,000*0.0005=5

Write 108 in exponential form using only prime numbers as a base​

Answers

Two to the second power times three to the third power

5x≥25 help th bewbsanks

Answers

X is greater than or equal to 5




To get this answer, we simply divide by five on both sides to isolate x

Mr. Thorbes bought a new journal for his poetry. If the journal normally cost $22 but was on sale for 20% off, how much did Mr. Thorbes save?

Answers

Answer:

He would save $4.40

Step-by-step explanation:

And in total he would pay 17.60

complete the table below to show the differences bettween algebraic expression and equation

Answers

Complete the table below to show the differences between algebraic

expression and equation.

Describe each to show their differences.

Give 3 examples of each.

Answer:

Explained below with examples

Step-by-step explanation:

1. Algebraic expression in mathematics are basically expressions that are formed from variables, integer constants, and also algebraic operations.

Examples include;

>> 2x² − xy

>> 3ab + 2b²

>> x² + y²

2. An algebraic equation is a phrase where the two sides of the equation which are the left and right hand sides are connected by the equal to sign (=).

Examples are;

>> 3y - y² = 2y² + 2

>> 3x - 4y = x + 2

>> 5a + 3b = 2b - 1

What is the ratio in simplest form between the length of a side in ABCD and the length of its corresponding side in WXYZ?

a.2\3
b.1\2
c.3\4
d.6\5

Answers

Answer:

The Answer would be C) 3/4

Step-by-step explanation:

If you subtract a quarter of the number presented on right left hand on the picture you get the numbers presented on the left hand side of the picture shown. There fore the ratio is 3/4 or three quarters of the already existing number.

Tina constructed triangle XYZ.

Which two words describe triangle XYZ?
A. equilateral and right
B. equilateral and isosceles
C. isosceles and scalene
D. isosceles and right

Answers

Answer:

It's D... Isosceles and right

Step-by-step explanation:

got it right on the quiz.

Apples weighing 30 pounds are placed in a crate that weighs p pounds. Which equation can
be used to find t, the total weight of both the crate and the apples in pounds?
A. t=30p
B. t=p+30
C. t=p-30
D. t=30-p

Answers

Key words: total
Total = add
B

Determine whether the given equation has one solution, no solution, or infinitely many solutions. 2 - 3(x+ 4) = 3(3 - x) cannot be determined one solution Ono solution infinitely many solutions. ​

Answers

Answer:

no solution

Step-by-step explanation:

The given equation is :

2 - 3(x+ 4) = 3(3 - x)

We need to solve the equation. It can be done as follows :

2-3x-12 = 9-3x

As -3x gets canceled from both sides. It means the given equation has no solution.

does anyone else play woozworld? if so, add me SummerRae0

Answers

Ok I will add u to if you can help me with my test

A book costs $1.49 and is sold in a retail store for $8.99. What is the percentage in mark up? *​

Answers

Answer:

603.35%

Step-by-step explanation:

Given that a book costs $ 1.49 and is sold in a retail store for $ 8.99, to determine what is the percentage in mark up, the following calculation must be performed:

1.49 = 100

8.99 = X

8.99 x 100 / 1.49 = X

899 / 1.49 = X

603.35 = X

Thus, the mark up percentage of the book is 603.35%, which implies an increase of more than 6 times its initial value.

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