if two identical dice are rolled n successive times, how many sequences of outcomes contain all doubles (a pair of 1s, of 2s, etc.)?

Answers

Answer 1

1 sequence of outcomes that contains all doubles when two identical dice are rolled n successive times.

There are 6 possible doubles that can be rolled on a pair of dice (1-1, 2-2, 3-3, 4-4, 5-5, 6-6).

Let's consider the probability of rolling a double on a single roll:

The probability of rolling any specific double (such as 2-2) on a single roll is 1/6 × 1/6 = 1/36 since each die has a 1/6 chance of rolling the specific number needed for the double.

The probability of rolling any double on a single roll is the sum of the probabilities of rolling each specific double is 1/36 + 1/36 + 1/36 + 1/36 + 1/36 + 1/36 = 1/6.

Let's consider the probability of rolling all doubles on n successive rolls. Since each roll is independent the probability of rolling all doubles on a single roll is (1/6)² = 1/36.

The probability of rolling all doubles on n successive rolls is (1/36)ⁿ.

The number of sequences of outcomes that contain all doubles need to count the number of ways to arrange the doubles in the sequence.

There are n positions in the sequence, and we need to choose which positions will have doubles.

There are 6 ways to choose the position of the first double 5 ways to choose the position of the second double (since it can't be in the same position as the first) and so on.

The total number of sequences of outcomes that contain all doubles is:

6 × 5 × 4 × 3 × 2 × 1 = 6!

This assumes that each double is different.

Since the dice are identical need to divide by the number of ways to arrange the doubles is also 6!.

The final answer is:

6!/6! = 1

For similar questions on sequence

https://brainly.com/question/7882626

#SPJ11


Related Questions

What is the line of reflection for the trapezoids?

On a coordinate plane, trapezoid A B C D has points (5, 4), (6, 4), (8, 3) and (5, 3). Trapezoid A prime B prime C prime D prime has points (1, 4), (0, 4), (negative 2, 3), (1, 3).

Answers

Answer:I believe it’s A(x=3)

Step-by-step explanation:

Calculate the slope of the line that contains the points (-3, -2) and (7, 2)

Answers

Answer:

the slope= 2/5        

the slope is 2/5

use the formula (y2-y1)/(x2-x1) to get the slope

Just need answer for both

Answers

..............................,..

Answer:

First one: 12 ft

Second one: 50ft^2

Step-by-step explanation:

Because both triangles are congruent, any value on one triangle is the same one on the other triangle so CBD= 12ft for the perimeter

Second one:

because both triangles are congruent like I stated above, both triangle are congruent.

But in this case we have to find the area of the whole rectangle.

What we do here is multiply 25 by 2

or

add 25+25

our answer is 50ft^2

Jacy has​ $1,000 to invest in either a fund that pays approximately​ 4.6% per year or in a savings account with an annual interest rate of​ 1.8%. Write a polynomial function​ S(x) to represent the interest Jacy will earn in 1 year by investing x dollars in the fund and the remainder in the savings account.

Answers

Answer:

.046x

Step-by-step explanation:

Eight less than 7 times a number is -29.​

Answers

Answer:

7x-8=-20

Step-by-step explanation:

Factorise x²+8x+12plz give answer ​

Answers

Answer:

(x+6)(x+2)

Step-by-step explanation:

we have

ax²+bx+c

To factor parabolas we need to find a number that adds to b (or 8) and mulitplies to a*c (or 12)

The numbers 6 and 2 fit this criteria which means we have

(x+6)(x+2)

Answer:

i.d.k the answer so sorry

Step-by-step explanation:

knkn

Andre has 5 notebooks. Each notebook contains 60 sheets of paper. How many total sheets of paper does Andre have in his notebooks?

Answers

Answer:

5 x 60 = 300 pages

Step-by-step explanation:

Answer:

5x60=300

Step-by-step explanation:

If he has 5 note books with 60 pages each he has 300 pieces of paper

Can someone help me with my homework

Answers

Answer:

lol i ltterally don't know what this is and im in algebra

Step-by-step explanation:

Answer:

1. Angle EFC and DCF

2.  All angles of a parallelogram add up to 360 so 4x-15+127=180 degrees

3. (4) 150 degrees

4. P = 45 degrees

Step-by-step explanation:

Can someone help me please?! I’ll make you brainlest.

Answers

6256 I think I used a online calc sry if wrong

just answer please hurry

Answers

Answer:

2.7 pages and 1.7 pounds of rice

Step-by-step explanation:

2.7 pages in one minute because 27/10=2.7

and 1.7 pounds of rice can be purchased for a dollar because 15/9 is about 1.7

retail price= $120
markup percent= 40%
what is the original cost

Answers

I believe it would be 72

Emir's Ice Cream Shop sold 1 sundae with nuts and 7 sundaes without nuts. What is the ratio of the number of sundaes with nuts to the total number of sundaes?​

Answers

Answer:

1:7

Step-by-step explanation:

divide 450 in the ratio 2 is to 3 is to 5​

Answers

Answer:

90 : 135 : 225

Step-by-step explanation:

sum the parts of the ratio, 2 + 3 + 5 = 10 parts

Divide the number by 10 to find the value of one part of the ratio

450 ÷ 10 = 45 ← value of 1 part of the ratio, then

2 parts = 2 × 45 = 90

3 parts = 3 × 45 = 135

5 parts = 5 × 45 = 225

Then

450 in the ratio 2 : 3 : 5 is 90 : 135 : 225

g(3) =
g(-2) =
g(0) =
9(-1) =
g(8)
g(-4)

PLEASE HELPPP!!!

Answers

Answer:

-4 Cot (−45)-4cot(-45)Sin (330)sin(330) Csc (60)

Step-by-step explanation:

Ms. Brown bought 6 boxes of pencils with a total of 240 pencils. How many pencils were in each box?

Answers

Answer:

40

Step-by-step explanation:

You need to divide 240 by 6 since there are 6 boxes and 240 pencils. If you do that, you will get 40. Hope it helps :)

Answer:

40

Step-by-step explanation:

240/6=40

Find the value of x and y.

Answers

Answer:

This is a triangle with 2 equal angles and equal to 60

=> this is an equilateral triangle

=> y = 60

    4x.3 = 54

=> y = 60

    x = 54/12 = 4.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

if two angles are 60 degrees, the third one is also 60 degrees

that means all the sides are equal

if one side is 4x

4x+4x+4x=54

12x=54

x=4.5

Sam owns a chain of fast food restaurants that operated 200 stores in 1999. If the rate of increase is 8% annually, how many stores does the restaurant operate in 2007?

Answers

Answer:

370 stores

Step-by-step explanation:

Given data

initial number of stores P= 200

r= 8%

t= 1999-2007=  8 years

Let us apply the compound interest expression to find the final amount of stores

A= P(1+r)^t

A= 200(1+0.08)^8

A= 200(1.08)^8

A= 200*1.85

A=370

Hence the number of stores in 2007 is 370 stores

65°
(х + 72)
i need help with x

Answers

Answer:

65x+4680

Step-by-step explanation:

E
C
5
4
9
B
D
C
Solve for x

Answers

Que se debe hacer es una pregunta???

is a parallelogram with 4 congruent sides a square ?​

Answers

Answer:

oopppppp yes

Step-by-step explanation:

Answer:

Yes

Good luck, and have the most amazing day!

Cheryl signs up for a savings account that guarantees an increase in her savings at a fixed rate of $15 per month. She plans to withdraw the money when it is more than twice the original amount of $200. Find the least number of complete months that Cheryl has to keep the money in the account for.

Answers

Answer: 14 months.

Step-by-step explanation:

Given: Original amount = $ 200

Fixed rate of growth = $15 per month

Let x be the number of months that Cheryl has to keep the money in the account for.

Then, [tex]200+15x=2(200)[/tex]

[tex]\Rightarrow\ 200+15x>400\\\\\Rightarrow\ 15x >400-200\\\\\Rightarrow\ 15x>200\\\\\Rightarrow x>\dfrac{200}{15}\\\\\Rightarrow x>13.333333\\\\\Rightarrow\ x=14[/tex]

Hence, it will take 14 months .

Consider 3y+6x+3 in the form y= ax+b. Find the constants a and b.

Answers

Answer:

a= -2 and b= 0

Step-by-step explanation:

Sorry the picture is a bit blurry

What is the average rate of change of g over the interval [-2,4]

Answers

Answer:

3

Average = sum of all the observations

Total number of observations

Average = 2+4

2

Average = - 6

2

3

possible number of learners in the
in a village, the bell rings every 30 minutes at the Junior School and every 40
minutes at the High School Both schools start lessons at 8:00 am
At what times between 8.00 am and 2.30p.m do the bells both rring

Answers

Find multiples of 30 and 40:

30: 30, 60, 90, 120, 150

40: 40, 80, 120, 160

The least common multiple is 120, so every 120 minutes they willl both ring.

1 hour = 60 minutes:

120/60 = 2 hours.

The bells ring together every 2 hours.

8 + 2  = 10 am

10 +  = 12pm

12 + 2 = 2 pm

The bells will ring together at am, 12 pm and 2 pm.

Answer:

Solution :-

At first common multiple of 30 an 40

[tex] \sf \to \: 30 = 30,60,90,120[/tex]

[tex] \sf \to \: 40 = 40,80,120[/tex]

Common Multiple = 120

Time taken = 120/60 = 2 hrs

Now,

8.00 + 2 = 10.00 am

10.00 + 2 = 12.00 noon

12.00 + 2 = 2.00 pm

[tex] \\ [/tex]

Pls help me with this my sister’s going to take my phone in 10 minutes and I will give brainleast

Answers

Answer:

What are the closer two numbers together the then you find the slope

Step-by-step explanation:

Answer:

1x-6

Step-by-step explanation:

Slope Form: Mx+b

Slope Formula: y2-y1/x2-x1

(4,-2) (5,-1)

-1-(-2)= 1

5-4=1

1/1=1

Y-intercept: -6

Hope this helps!

When the points plotted on a graph that are joined together produce a straight line, which graph do we obtain

Answers

Answer:

linear graph

Step-by-step explanation:

if the points are coming in a straight line it is linear

(Grade 7 math) What is the area of the triangle when b=3.5 and h=3? B is the base and h is the height

Answers

Answer:

The area of the triangle

    A = 5.25 square units

Step-by-step explanation:

Explanation:-

Given that the base of the triangle(b) = 3.5

The height of the triangle(h)  = 3

The area of the triangle

                                 [tex]A = \frac{1}{2} base X height[/tex]

                                [tex]A = \frac{1}{2} (3.5) (3)[/tex]

                               A = 5.25 square units

7 + 9 divided by 2
zzzzzzzzzzzzz
Pewdie-pie coco-melon dis-track cause yt banned. You can find it on StilBS chan.nel

Answers

Letssss gooooooooooooooo
Also (8)

Solve for x: 5x – 2 = 13
GIVING BRAINLIST!! Please help

Answers

Answer:

3

Step-by-step explanation:

5x - 2 = 13

+2        +2

5x = 15

÷5  ÷5

x = 3

Have a great day <3

Answer:

x=3

Step-by-step explanation:

Is one-half of a square smaller than one-quarter of the same square? How do you know?

Answers

Answer:

No

Step-by-step explanation:

one-half is bigger than one-quarter of the same square

Other Questions
Hello! So I have been practising some coding, however, there seems to be an error in my code. I have been trying to figure out what is wrong, however, I just can't seem to find it. There is no syntax error but, there seems to be a problem with my input. I am currently using repl.it and I am making a calculator. I would input something like "multiply" however, the calculator would only square. I have tried changing the variables but it just keeps coming back to the first "if" statement. I would appreciate some help. I need help pleaseee): What are your guy's opinion on this intro for an essay and what would you change Title: A Dogs Best FriendIntro: We all know that a man's and woman's best friend is a dog, but who is a dog's best friend? Is a dog's best friend its owner, the mailman, or maybe another dog, it depends on the relationship. is 250% of 41 less than 100, greater than 100 but less than 150, or greater than 150? What are the zeros of f(x) = x2 - x - 30?O A. x = 10 and x = -3O B. x = 6 and x = -5O C. x= -10 and x = 3O D. x= -6 and x = 5 what useful purpose is served by cell division in a multicellular organism : select all the correct answers. A: to ensure that a cell does not become to large B; To produce new cells during an organisms growth C: To replace damaged cells and tissues D: to ensure all cells remain undifferentiated Mae Ling earns a weekly salary of $345 plus a 7.0% commission on sales at a gift shop. How much would she make in a work week If she stood $4,300 worth of merchandise? She would make $________? Cu + HNO3 --> Cu(NO3)2 + NO + H2Ohow to balance... WILL GIVE 15 POINTS HELP ASAP PLS. Which of the following best describes the relationship between air temperature and relative humidity?A. Cold air cannot hold any water vapor.B. Warm air can hold less water vapor than cold air.C. Cold air can hold less water vapor than warm air.D. Warm air and water vapor are measured in degrees Celsius (C). Will mark brainliest for whoever answers 1, 1/2, 1/4, 1/8, ... What's the pattern rule and the next three numbers? Please someone help me! Pls help ASAP if you can please Help plz...plz dont steal points.. What type of device is a keyboard? Input Memory Output Storage I AM LITERALLY CRYING RIGHT NOW PLEASEE HELPPP WILL MARK BRANLIEST HELPPP MEEPart 1: ExploreBased on your research and observations of the three common states of matter, answer thefollowing questions.Out of the videos, animations, and images you researched, which was your favorite? Why?Do you feel it accurately represented the differences between each state of matterHow does the space between the particles in each state of matter differ?How do the particles in each state of matter move? Part 2: ExplainExamine the heating curve of water below, and then answer the questions about it. If you require the use of a text reader, open the file Heating Curve of Water to receive the information.Which three parts of the graphs curve represent the solid, liquid, and gaseous state of water?Explain your reasoning. Which point of the graphs curve represents the melting point of water? Explain your reasoning.Which point of the graphs curve represents the boiling point of water? Explain your reasoning.What happens to the energy of water in Part B and Part D of the graphs curve? How do you know?Why does the temperature of the water stay the same when it melts and boils?Now comes the hands-on part of your project! You will continue to explore phase changes by performing an experiment and creating your own heating curve. Before you begin your experiment, read over the following information. The materials you will need for your experiment are listed below.small potmeasuring cup (must have mL and oz markings)spoon (wooden, plastic, or metal)icewaterstovethermometer (should have units in CTime (min) Temperature of Water (C) Observations of Water0123456789101112131415Place 14 oz of crushed ice into a small pot. Then add about 125 mL of water to it.Using the thermometer, measure and record the initial temperature of the ice water. List this temperature in C in the 0 minutes row of your data table in the lab handout. *Do not allow the thermometer to touch the bottom of the pot when recording measurements.Place the pot on the stove, and turn the knob to the medium-low setting.Using the thermometer, measure the temperature every minute until the water begins to boil vigorously. Record this data in the table on your lab handout.At each measurement, also record what is happening to the water. Be sure to record the times of these events:The ice melts.The water forms steam.The water begins to boil.Once the water has begun to boil, stir the water constantly with the spoon.Continue to measure and record the temperature every minute until almost all the water has boiled and the pot is close to empty.Record the last temperature, and turn off the stove. DO NOT TOUCH THE POT WITHOUT SAFETY EQUIPMENT.Create the x-axis and y-axis of a graph.Label the x-axis as follows: Time (min).Label the y-axis as follows: Temperature of Water (C).Along the x-axis, create and label 15 marks, one for each minute of the experiment. (Hint: The origin starts at 0.)Along the y-axis, create and label temperature markings for every 20 degrees. (Hint: The origin starts at 0.)Refer to the data from your experiment to plot the points on your graph. Then connect each of the data points with a line.Look over your graph to make sure it is clear and correctly labeled.Either save your graph as a computer file, or take a picture of your graph and upload it as a file on your computer.Describe your experience in performing the experiment. What went well? What could have beenimproved?Examine your line graph. How does the graphs slope change over time?Examine your line graph. Why does the slope change?How could you apply the knowledge gained from this experiment in the real world?Hint: Think of cooking.Make a prediction. How do you think adding other substances to the water would affect itsheating curve?THANK YOU SO MUCH please help me , I'm so confused ... Fill in the question Why did Thomas Jefferson oppose Hamiltons national bank?He thought it would be too weak.He thought it was unconstitutional.He wanted a more powerful government.He believed in the implied powers of the Constitution. Please help if you want brianleist! Thank You!! Donald (age 22) attended college at night while working to support his forty five year old mother. He was in love with a girl whom he hoped to marry. Donald's mother, however, did not like the girl and tried to break them up. The girl could see that Donald would never be able to support both her and his mother. She also knew that the three of them could never get along together under the same roof. She gave Donald a month to decide what to do about it. A week before the deadline, he suddenly disappeared. He was found two weeks later in another state, completely unable to say who he was, where he was, or what he was planning to do. He could not recall, or even recognize, the name of either his mother or his girl friend. Obviously this was his solution to the conflict. This behavior was not inconsistent with his previous history. In his earlier school days, he had frequently forgotten his homework and been absent minded. Forgetting things was already a convenient habit for him.