We roll two fair 6-sided dice. If a fair dice is rolled, the probability of it landing on any number between [1-6] is equi- probable (i.e., 1 6 ). (a) Find the probability that doubles are rolled. (Rolling doubles mean both dices land in the same number, e.g., 3 and 3.) (b) Given that the roll results in a sum of 6 or less, nd the conditional probability that doubles are rolled. (c) Find the probability that the larger of the two die's outcomes is at least 4.

Answers

Answer 1

Answer:

a.) [tex]\frac{1}{6}[/tex]

b.) [tex]\frac{3}{15}[/tex]

c.) [tex]\frac{27}{36}[/tex]

Step-by-step explanation:

Given - We roll two fair 6-sided dice. If a fair dice is rolled, the probability

             of it landing on any number between [1-6] is equi- probable

             (i.e., [tex]\frac{1}{6}[/tex]).

To find - (a) Find the probability that doubles are rolled.

               (b) Given that the roll results in a sum of 6 or less, and  

                    the conditional probability that doubles are rolled.

               (c) Find the probability that the larger of the two die's outcomes

                    is at least 4.

Proof -

As given , two fair 6-sided dice is rolled.

The sample space is as follows :

S = { (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

        (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

        (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

        (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

        (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

        (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)  }

Total number of outcomes = 36

a.)

Sample space that double are rolled = { (1, 1), ( 2, 2), ( 3, 3) , ( 4, 4), ( 5, 5), ( 6, 6) }

Total number of possible outcomes = 6

So, Probability = [tex]\frac{6}{36}[/tex] = [tex]\frac{1}{6}[/tex]

b.)

Sample space that roll shown sum of 6 or less = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (5, 1)}

Now,

Total outcomes = 15

Total possible outcome that doubles are rolled = 3 ( i.e (1,1), (2, 2), (3, 3) )

So, Probability = [tex]\frac{3}{15}[/tex]

c.)

Sample space that larger of the two die's outcomes is at least 4 = { (1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6) }

Total possible outcomes = 27

So, Probability = [tex]\frac{27}{36}[/tex]


Related Questions


New York is 5 hours behind London. It is 15:55 in London,
what time is it in New York using the 24 hour clock?

Answers

Answer:

10:55

Step-by-step explanation:

15:55 - 5 = 10:55

RIP my points went down alot ;-; gived away 1k+ points today. sry i couldnt give more. ill give brainliest to first person that answered

Answers

Heya, how are you doing today ^-^

A labor dispute has arisen concerning the distribution of 20 laborers to four different construction jobs. The first job is considered to be very undesirable and requires 6 laborers. The second, third and fourth jobs require 4, 5 and 5 laborers, respectively. The dispute arose over an alleged random distribution of the laborers to the jobs that placed all 4 members of a particular ethnic group on job 1. In considering whether the assignment represented injustice, a mediation panel desired the probability of the observed event. Determine the number of sample points in the sample space S for this experiment. That is determine the number of ways the 20 laborers can be divided into groups of the appropriate sizes to fill all of the jobs. Find the probability of the observed event if it is assumed that the laborers are randomly assigned to jobs.

Answers

Answer:

The answer is "0.30%"

Step-by-step explanation:

To assign employees to work, we have to select 6 out of 20 to do work, instead select 4 out of another 14 jobs, 2 to do, and 5 out of another 10 works 3. The other five were going to go do work four. They may decide how often ways of making each of these options. Their service would be how many forms to allocate those four positions to staff. The random sample is from the height.

There are equally estimated that numbers of arrangements with both the four in Job 1.They then allocate all four to work 1. In this situation We must then select 2 out from the 16 existing spaces in job 1, 4 out from the 14 remaining spaces in job 2, 5 out of the 10 existing spaces in job 3 as well as the ones remaining in job 4.

The possibility of any four being at 1 is that they've been all divided by the overall amount of circumstances in 1 task.

[tex]\to \frac{[ \frac{16!}{(2!4!5!5!)}]}{[\frac{20!}{(6!4!5!5!)}]}\\\\\to [ \frac{16!}{(2!4!5!5!)}] \times [\frac{(6!4!5!5!)}{20!}]\\\\\to [ \frac{16!}{(2!)}] \times [\frac{(6!)}{20!}]\\\\\to [ \frac{16!}{(2!)}] \times [\frac{(6\times 5 \times 4 \times 3 \times 2!)}{20!}]\\\\\to 16! \times [\frac{(360)}{20 \times 19 \times 18 \times 17 \times 16!}]\\\\\to \frac{(360)}{20 \times 19 \times 18 \times 17 }\\\\\to \frac{(360)}{20 \times 19 \times 18 \times 17 }\\\\\to \frac{360}{116,280}[/tex]

[tex]\to 0.00309597523 \approx 0.30 \%[/tex]

8x+5x^3-5 write polynomial in standard form, Then name the polynomial based on the degree and number of terms

Answers

Answer:

wag na baka imyday mo pa

Step-by-step explanation:

hahahahahahahahahahahahahahahahahaahhaahahahahahhahahahahahahahahahahahahahahahahahahahahahahahahhahahahah ahahahahahahaha ahahahahahahaha ahahahahahahaha hahahahahah ahahahahahahaha

How long will it take me to read 125 pages if I can read 20 pages in 30 minutes?

Answers

Answer:

187.5

Step-by-step explanation:

Christine Wong has asked Dave and Mike to help her move into a new apartment on Sunday morning. She has asked them both, in case one of them does not show up. From past experience, Christine knows that there is a 55% chance that Dave will not show up and a 45% chance that Mike will not show up. Dave and Mike do not know each other and their decisions can be assumed to be independent. a. What is the probability that both Dave and Mike will show up

Answers

Answer:

a) 26.79%, b) 50.42% and c) 22.79%

Step-by-step explanation:

a. What is the probability that both Dave and Mike will show up?

As decisions of showing up can be assumed to be independent, the probability will be given by

(1-0.53)(1-0.43)=(0.47)(0.57)=0.2679=26.79%

b. What is the probability that at least one of them will show up?

There are two possibilities for this to happen:

Dave shows up but Mike does not. The probability of Dave to show up is (1-0.53)=0.47 and the probability that Mike does not is 0.43. Then, as these events are independent, the probability for both of them to happen is (0.47)(0.43)=0.2021=20.21%

Mike shows up but Dave does not. The probability of Mike to show up is (1-0.43)=0.57 and the probability that Mike does not is 0.53. Then, as these events are independent, the probability for both of them to happen is (0.57)(0.53)=0.3021=30.21%

Therefore, the probability that at least one of them will show up? is 20.21%+30.21%=50.42%.

c. What is the probability that neither Dave nor Mike will show up?

As decisions of showing up can be assumed to be independent, the probability will be given by

(0.53)(0.43)=0.2279=22.79%

ILL MARK AS BRAINLEST
Twice Carrie’s age increased by three is equal to twenty-five. Which equation can be used to find Carrie’s age, x?

A.
2(x + 3) = 25

B.
2(3) + 25 = x

C.
2x + 3 = 25

D.
x + 2(3) = 25

Answers

Answer:

im pretty sure the answer is c

2. Find the area of a circle with a radius of 5 meters. A circle with a radius of 5 meters has an area of

Answers

Answer:

A=πr2=π·52≈78.53982m²

Step-by-step explanation:

Answer:

78.57 m^2

Step-by-step explanation:

answer is 78.57

pls solve ii need it

Answers

Answer:

multiply each decimal

Step-by-step explanation:

Answer:

1.144

Step-by-step explanation:

multiply 1.1x0.8x1.3

Convert the equation to vertex form.
y = x2 – 8x + 10

Answers

Answer:

Step-by-step explanation:

y = (x² - 8x) + 10

Complete the square

 coefficient of the x term: -8

 divide it in half: -4

 square it: (-4)² = 4²

 use 4² to complete the square and keep the equation balanced:

y = (x²-8x + 4²) - 4² + 10

y = (x-4)² - 6

Answer:

y = (x - 4)² - 6

Step-by-step explanation:

use the 'completing the square' method:

x² - 8x + 10 = 0

x² - 8x + 16 = -10 + 16

(x - 4)² = 6

y = (x - 4)² - 6

Determine the graph that represents a function.

Answers

3rd one there cant be anything under or over a line so it cant be the circle or the parabola so it has to be the 3rd one
the function would be the third graph. to find out if a graph is a function do something called a vertical line test. basically take a pencil or something straight and out it vertically against the graph then push it along the graph. at each given point there should only be one point. so the first two would not pass the vertical line test

Simplify: (2x + 8)(7x2 - 9x - 5)

Answers

Answer:

-18x^2 -54x + 72

Step-by-step explanation:

(2x+8)(7x2-9x-5) simplifies to -18x2−54x+72

Maria found a circular rug for her floor. The rug has a circumference of 50.24 inches. Which formula should Maria use to help her find the diameter of the rug?

Answers

Answer:

She should use the formula [tex]C = \pi d[/tex] to find a diameter of 16 inches.

Step-by-step explanation:

The circunference of a circle is given by:

[tex]C = 2\pi r[/tex]

In which r is the radius, which is half the diameter. So, it can also be given by the following formula:

[tex]C = 2\pi \frac{d}{2} = \pi d[/tex]

In which d is the diameter.

Which formula should Maria use to help her find the diameter of the rug?

She should use this formula:

[tex]C = \pi d[/tex]

Since the circunference is 50.24 inches, the diameter will be of:

[tex]d = \frac{C}{\pi} = \frac{50.24}{\pi} = 16[/tex]

WILL MARK BRAINLEST PLS HELP ME Find the area of the circle. Round to the nearest tenth. Use 3.14 for it.
32 m
The area of the circle is about
m2.

Answers

Answer:

[tex]804.3m^2[/tex]

[tex]\pi *16^2=804.24772[/tex]

PLZ HELP PLZ HELP

SELECT ALL MEASURMENTS THAT ARE ABOUT 1 YARD LONG


Length of student desk

Height of classrom'

Width of classroom door

Height of building
Length of a movie ticket

Answers

Answer:

c

Step-by-step explanation:

a certain antihistamine is often prescribed for allergies. a typical dose for a 100-pound person is 21 mg every 6 hours.
a. how many 12.7 mg chewable tablets would be taken in a week?
b. this antihistamine also comes in a liquid form with a concentration of 12.7 mg / 6 ml following the prescribed dosage how much liquid antihistamine should a 100-pound person take in a week?​

Answers

Answer:

a)46 tablet approx

b)277 ml approx

Ethan tired to write an equation of the linear table but made a mistake. Need help it’s due today!?!?

Answers

Given:

The table for a linear function.

To find:

The equation of the linear function.

Solution:

If a linear function passes through two points, then the equation of linear function is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Consider any two points from the given table. Let the two points are (2,-2) and (4,0). So, the equation of linear function is

[tex]y-(-2)=\dfrac{0-(-2)}{4-2}(x-2)[/tex]

[tex]y+2=\dfrac{2}{2}(x-2)[/tex]

[tex]y+2=x-2[/tex]

Subtracting 2 from both sides.

[tex]y+2-2=x-2-2[/tex]

[tex]y=x-4[/tex]

So, Ethan 's made a mistake. The sign between x and 4 must be negative but in Ethan's equation it is a positive sign, which is not correct.

Therefore, the required linear equation is [tex]y=x-4[/tex].

1 of 12
Eli is following this recipe to bake bread rolls.
He uses 500 g of flour.
How much of the other ingredients does he use?
Recipe: Makes 12 bread rolls
400 g flour
6 g salt
8 g yeast
40 mL oil
360 ml water
g salt
g yeast
mL oil
mL water

Answers

Answer:

360

Step-by-step explanation:

&$5%4645$655$456&&&66

Suppose that You had launch the message 6.75 feet west from the edge of the ravine Instead of 5 feet west from the edge of the ravine would the message make it across the ravine show your work and explain your answer

Answers

Answer:

6.75 times 5 would be 17.1

Step-by-step explanation:

Divide.

68, 302 divided by 1,000

Enter the exact quotient.

Answers

Answer:

68.30200

Step-by-step explanation:

The exact quotient of 68,302 ÷ 1000 is 68.302.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

68,302 ÷ 1000

= 68,302 / 1000

= 68.302

Thus,

The quotient is 68.302.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ5

What is the product?
(X^4)(3x-2)(4x2 +5x)?

Answers

Answer:

12x^7+7x^6-10x^5

Step-by-step explanation:

(X^4)(12x³+15x²-8x²-10x)

(X^4)(12x³+7x²-10x)

12x^7+7x^6-10x^5

-4-2-2) - 2x + 5 = 31

Answers

Answer:

2x+5=31 is the most common correct answer

Please Helppplpppppp

Answers

Answer:B
I hope this helps and have a great day!

1a) solve the equation

Answers

Which equation, please list the equation
Where is the equation? .....

Three angles of a quadrilateral are 75,120, 90,then the fourth angle..​

Answers

Answer:

75

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Geometry

Sum of Angles in a Quadrilateral: 360

Step-by-step explanation:

Step 1: Set up

75 + 120 + 90 + ∠4 = 360

Step 2: Solve

Add:                                                                                                                   285 + ∠4 = 360[Subtraction Property of Equality] Subtract 285 on both sides:                   ∠4 = 75

I need help with this whoever can get it right I will mark you brainlest

Answers

the answer is c. 72cm^2

for each section of the prism you multiply the length times the width and then add all of the numbers together to get 72
72cm^2!!!!! Your welcome

Jacob bought 9 bags of balloons. Each bag has 25 balloons. He fills all the balloon and puts 5 balloons in each bunch. How many bunches can he make please help me

Answers

45
9 x 25 = 225
225 divided by 5= 45
So Jacob can make 45 bunches
Hopefully I’m right :)

John and Adam are selling candy. John sells 6 pieces of candy for $10. Adam sells 13 pieces of candy for $20. Whose candy costs less?

Answers

Adam,
because for John if you add 6+6 = 12 for 20 dollars where Adam has 13 for 20

Answer:

John sells candy at the lowest price.

Step-by-step explanation:

If John sells 6 candies at 10$, then that's what's called a ratio between the price and the candy. We can double the amount of candy and the price to $20 for each 12 candies, $30 for 24, $40 for 36, etc. But it would still maintain the ratio of 6 candies for each 10$. Adam however, sells candy at 13 pieces for $20. We can divide the ratio down to 6.5 candies for 10$. But since we "can't" split a candy in half, we'll round it to 7 pieces for 10$, which costs more than 6 for 10$: Therefore, John sells candy at the lower price.

The number of goats in a farm increases by 5 goats each year. If the farm has a population of 20 goats after the first year, and n denotes the number of years, which recursive equation gives the population of goats, , as a function of the year?

Answers

Answer:

f ( 1 )= 20; f ( n )= f (n - 1) + 5, for n > 2

(the > has a line under it)

Step-by-step explanation:

Answer:

f (1) = 20; f (n) = 2 · f (n - 1) - 0.3 · f (n - 1) + 5, for n ≥ 2

Step-by-step explanation:

The other person left some numbers out.

Which of these systems of equations has an infinite number of solutions?

Answers

Answer: The first one

Step-by-step explanation:

-6c + 11d = 20

-6c + 11d = 20

They're the same equation meaning they'll be on the same line. They would have infinite solutions.

Answer: The first one

Step-by-step explanation:

-6c + 11d = 20

-6c + 11d = 20

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