What is the probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, i = 2, 3,. , 12?.

Answers

Answer 1

Answer:

0, 1/18, and 1/36

Step-by-step explanation:

For i = 2, the probability it lands on 6 is 0, because you cannot sum to 2 with a 6. The same applies to i = 3 thru i = 6.

For the probability that at least one of a pair of fair dice lands on 6 for i = 7, there are only two possible ways, the first roll is a 6 and the second roll is a 7, and the first roll is a 1 and the second roll is a 6. The total amount of ways is 6 * 6 = 36, so the total probability is 1/18. This also applies to i = 8 thru i = 11.

For i = 12, there is only one way to get 12, the first dice lands on 6 and the second dice lands on 6. Assuming the dice are indistinguishable, the probability is 1/36.

Answer 2

The probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, where i ranges from 2 to 12, is 23/12.

We have,

The complementary probability of "at least one die lands on 6" is "neither of the dice lands on 6."

Therefore, you need to find the probability that neither of the dice lands on 6 for each possible sum i, and then subtract that probability from 1 to get the desired probability.

Let's go through the cases:

i = 2 (only possible sum with two dice):

In this case, both dice must show a 1.

The probability of this happening on a fair 6-sided die is

(1/6) * (1/6) = 1/36.

i = 3: The combinations are (1, 2) and (2, 1).

The probability of either happening is 2 * (1/6) * (1/6) = 1/18.

i = 4:

The combinations are (1, 3), (2, 2), and (3, 1).

The probability of any of these happening is 3 * (1/6) * (1/6) = 1/12.

i = 5:

The combinations are (1, 4), (2, 3), (3, 2), and (4, 1).

The probability of any of these happening is 4 * (1/6) * (1/6) = 1/9.

i = 6:

The combinations are (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1).

The probability of any of these happening is 5 * (1/6) * (1/6) = 5/36.

i = 7:

The combinations are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1).

The probability of any of these happening is 6 * (1/6) * (1/6) = 1/6.

i = 8:

The combinations are (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2).

The probability of any of these happening is 5 * (1/6) * (1/6) = 5/36.

i = 9:

The combinations are (3, 6), (4, 5), and (5, 4).

The probability of any of these happening is 3 * (1/6) * (1/6) = 1/12.

i = 10:

The combinations are (4, 6) and (6, 4).

The probability of either happening is 2 * (1/6) * (1/6) = 1/18.

i = 11:

The combinations are (5, 6) and (6, 5).

The probability of either happening is 2 * (1/6) * (1/6) = 1/18.

i = 12:

The combination is (6, 6).

The probability of this happening is (1/6) * (1/6) = 1/36.

Now, sum up the probabilities for each case:

(1/36) + (1/18) + (1/12) + (1/9) + (5/36) + (1/6) + (5/36) + (1/12) + (1/18) + (1/18) + (1/36)

This simplifies to:

69/36 = 23/12

Thus,

The probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, where i ranges from 2 to 12, is 23/12.

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Related Questions

The product of −2 and a number x is greater than 30. Whats the solution of the inequality.


Answers

Answer:  x < -15

Step-by-step explanation:

(-2)*(x) > 30

x < -15  The inequality reverses direction when a negative number is used in the manipulation (we divided by -2).

expand the logarithm as much as possible using properties. please help!
log square root on 1,000,000x

Answers

Step-by-step explanation:

log (√1000000x)

Rewrite √1000000x as (1000000x)1/2.

expand long ((1000000x)1/2) by moving 1/2

oby moving logarithm.

1/2 longth (1000000x)

Rewrite

log

(1000000x) as log(1000000)+log(x).

1/2(log(1000000)+log(x))

Logarithm base 10 of 1000000 is 6.

1/2(6+log(x))

Apply the distributive property.

1/2.6+1/2 log(x)

Cancel the common factor of 2.

3+1/2 long(x)

Combine 1/2 and log(x)

3+ long(x)/2

Step-by-step explanation:

See the steps below:

[tex]log\sqrt{1000000x} =\\(1/2)log 1000000x=\\(1/2)log10^6+(1/2)logx=\\(1/2)(6) + (1/2)logx=\\3+(1/2)logx[/tex]

What is 121 divided by 18?

Answers

Answer:

6.7222222222

Step-by-step explanation:

This Maths Is Easy, Y Did You Post It?

Answer:

=6.7222222222

Step-by-step explanation:

Easy peesy lemon squezy!

In the first two hockey games of the year, Roland played 1 ½ periods In each of two games. How many periods in all did he play?

Answers

Answer:

2.42

Step-by-step explanation:

I AM VERY SORRY IF ITS WRONG

A ceramic artist can shape a pot in 3 minutes. It takes 10 minutes to fire one batch of pots in the kiln. If there are p pots in a batch, which expression represents the time it takes to shape and fire one batch of pots? How long will it take the potter to form and fire

Answers

Answer:

Your mom

Step-by-step explanation:

I saw her yesterday

Can anyone help, im stuck

Answers

Answer:

The second one is right

Step-by-step explanation:

anyone help, im stuck

Answer:

The third one

Step-by-step explanation:

Since, 1 can be represented by x we can make an equation

2 can be represented y

and 4 can be represented by x

Since x + y = 180 and x + z = 180

y = z

Or 2 = 4

Brainliest please :)

Ali walks 256km and Ahmed walks 112km. How much did they walk altogether? Give answer as a mixed number in its lowest term

Answers

Solution:Ali walks 2 5/6 km and Ahmed walks 1 1/2 km.Therefore, the distance they walked altogether

= (2 5/6+ 1 1/2) Km = (17/6+3/2) Km = 4 1/3 Km

Answer:

They walked 4 1/3 Km altogether.

Hope it helps.

Do comment if you have any query.

what would the answer be need help

Answers

Answer:

The equation would change to be f(x) = 12x + 50

Step-by-step explanation:

The equation given follows the form y = mx + b. In the equation, m = the charge in dollars per person, with x representing the amount of people, and b = the initial reservation fee.

This means that if you change the charge per person, the m value will change, and if you change the reservation fee, the b value will change.

Thus, your new equation will be f(x) = 12x + 50

` 10,800 for 3 years at 121 2% per annum compounded annually.​

Answers

Answer:

15,173.22

Step-by-step explanation:

Looks like there's a typo in the question.

Should it be:

10,800 for 3 years at 12% per annum compounded annually.​

-------------------------------

a = 10800 * (1.12)^3

a = 15,173.22

help me for brainlist

Answers

The line intersects x - Axis at 6

- BRAINLIEST ANSWERER

123, 472 to two decimal places​

Answers

Answer:

123.00 and 472.00

Step-by-step explanation:

can't really do much except add 0's since those numbers are whole numbers

which expression means the same as subtract from 7 and then multipy by 4

Answers

Answer:7-3x4 subtract 3 from 7 means you need to take 3 out of 7 (7-3) then you need to multiply that by 4! Hope this helped!

Step-by-step explanation:

Answer:

[7-3]4 or [7-3]x4 your welcome hope it helps!

Step-by-step explanation:

If £2000 is placed into a bank account that pays 3% compound interest per year,
how much will be in the account after 2 years?

Answers

£3880 is the answer after two years the amount will be 4000£ because 2000 x 2 =4000 and if it pays compound interest you would have to take 120 out of 4000 because 3% of 2000 is 60 so 60x2=120 4000-120=3880

parallel perpendicular or neither

Answers

Answer:

Parallel

Step-by-step explanation:

Line A can be simplified to 1/5x = y.

Line B can be simplified to y = 1/5x + 16.

They both have the same slope, 1/5, so they will be parallel.

Answer:

Parallel

Step-by-step explanation:

Same thing as the last one. Put it in [tex]y=mx+b[/tex]

A: [tex]y=1/5x[/tex]

and

B: [tex]y=1/5x+16[/tex]

These lines are parallel because they have the same slopes, but different y-intercepts.

John earned $12 a day for babysitting his siblings after school each weekday (he did not babysit on weekends). He liked to have a small amount of money to spend on treats at the school canteen that his parents refuse to buy, but he also wanted to build up some savings. John decided to put a fraction of his earnings into a jar straight away. He spent all the rest on canteen treats.


How much money did John earn over a nine week term?

After 9 weeks, John had $378 in his jar. What percentage of his money did he save?

Answers

Answer:

He earns $540

70% of his money went to savings

Step-by-step explanation:

9 weeks x 5 days a week = 45 days

45 days x $12 a day = $540

378 * 100 / 540 =  (378*100) / 540 =  37800/540 = %70

An auditorium seats 48 students per row. A total of 1665 students are in the auditorium today. All the rows are full except for the front row. a. How many rows are in the auditorium? There are rows in the auditorium.

Answers

1665/48 = 34.6875 rows

Since we know that these rows currently have students, we know that the auditorium has 35 rows with students. Since the front row is not full, it means there is an extra row.

36 rows

There are 35 rows in the auditorium.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

An auditorium seats 48 students per row.

And, A total of 1665 students are in the auditorium today.

Now,

Since, An auditorium seats 48 students per row.

And, A total of 1665 students are in the auditorium today.

Hence, Number of rows in the auditorium = 1665 / 48

                                                                 = 35

Thus, Number of rows in the auditorium = 35

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Kevin hiked 4 miles in 135 minutes. Which equation can be used to find how many hours it took Kevin to hike the 4 miles?

Answers

Answer:

135 divided by 4

Step-by-step explanation:

niomie bakes 24 cookies in 10 minutes. at this rate how many cookies can she bake in 30 minutes

Answers

Answer:

She can bake 72 cookies in 30 minutes

Step-by-step explanation:

24 · 3 = 72

Why are negative exponents not positive.

Answers

A positive exponent tell how many times to multiply the basement base number, and a negative exponent tells us how many times to divide the base number

1. What is the vertex for the following quadratic function, y = 2x^2 - 4x + 5?
A). (1,3)
B). (3, 1)
C) (0,5)
D). (2,5)

Answers

Answer:

A

Step-by-step explanation:

Given a quadratic in standard form

y = ax² + bx + c ( a ≠ 0 )

Then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = 2x² - 4x + 5 ← is in standard form

with a = 2 and b = - 4 , then

[tex]x_{vertex}[/tex] = - [tex]\frac{-4}{4}[/tex] = 1

Substitute x = 1 into the equation for corresponding value of y

y = 2(1)² - 4(1) + 5 = 2 - 4 + 5 = 3

vertex = (1, 3 ) → A

gergio ran 5 kilometers in 30min. If he ran at this same pace how many did he run each min

Answers

Answer:

6 minutes per kilometer

Find the value of Y - triangle measurments

PLEASE HELP! I WILL GIVE BRAINLIEST!

Answers

Answer:

y=8

Step-by-step explanation:

6y=8y-16

-2y=-16

y-8

congurnet side have congruen angles

NM=MP

[tex]\\ \sf\longmapsto <N=<P[/tex]

[tex]\\ \sf\longmapsto 6y=8y-16[/tex]

[tex]\\ \sf\longmapsto 8y-6y=16[/tex]

[tex]\\ \sf\longmapsto 2y=16[/tex]

[tex]\\ \sf\longmapsto y=8[/tex]

3/5 + (-4/11)...........

Answers

Answer:

13/55

Step-by-step explanation:

(3/5) + -(4/11) = (3/5) - (4/11) = (33/55) - (20/55) = (13/55)

Tell me if I'm wrong :)

[tex]\dfrac 35 + \left( -\dfrac 4{11} \right) \\\\\\=\dfrac35 - \dfrac{4}{11} \\\\\\=\dfrac{13}{55} \approx 0.24[/tex]

What is the following sum???? Please help ASAP

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The equivalent expression is ~

[tex]7 \bigg( \sqrt[5]{ {x}^{2}y } \bigg)[/tex]

just assume the whole thing in brackets as a single variable and perform addition ~

If two line are perpendicular which statement is true

Answers

The two lines intersect each other to make it perpendicular
Hope this helps you. Have a great day

If the ratio of grapes to walnuts to oranges is 6:6:12, how many grapes are there if the total number of fruits is 192?

Answers

Answer:

48 grapes,

Step-by-step explanation:

Firstly, let's sum up the ratio,

6+6+12=24

The fraction of grapes is therefore, 6÷24 or ¼

A ¼ of 192 is 48.

Signifying, there are 48 grapes.

A cheerilee teen willing to help,

stay positive, safe and Brainly!

Question:-

If the ratio of grapes to walnuts to oranges is 6:6:12, how many grapes are there if the total number of fruits is 192?

Answer:-

48 grapes

Explanation:-

look at the attached picture :)

Can someone help me please

Answers

Step-by-step explanation:

it just means to convert these equations into function definitions.

and a function looks like

y = ... something with x, factors, other functions, constants

1)

x + y = z

y = -x + z or z - x

2)

x - y = z

x - z = y or y = x - z

3)

x × y = z

y = z/x

4)

x/y = z

x = z × y

x/z = y or y = x/z

-10+2= (operation of integers)

Answers

Answer:

-8

Step-by-step explanation:

Hi there! :)

-10+2=-8

Hope this helps!

~Just a determined gal

#CarryOnLearning

Please mark brainliest; I would really appreciate that! :)

[tex]MysteriousNature :)[/tex]

expand the expression, image attached giving brainliest please help

Answers

(2m + n) (2n -m)

2m×2n-2m×m+n×2n-mn

4mn-2m^2 +2n^2-mn

4mn-mn-2m^2+2n^2

3mn-2m^2+2n^2

3 - k - 5k =3
i need help on this asap

Answers

Hello there!

3-k-5k=3

Combine like terms:

3-6k=3

-6k=3-3

-6k=0

k=0

Hope it helps!

~Just a determined gal

#CarryOnLearning

[tex]MysteriousNature[/tex]

Answer:

k = 0

Step - By - Step:

1. 3 - k - 5k = 3

3 - 6k =3

2. rearrange terms:

3 - 6k = 3

-6k + 3 = 3

3. Subtract  3 from both sides of the equation:

-6k_3=3

-6k+3-3=3-3

4. simplify:

-6k + 3 - 3 = 3 - 3

-6k = 3 - 3

-6k = 0

5. divide both sides of the equation by the same term:

-6k = 0

-6k/-6 = 0/-6

6. simplify:

k = 0/-6

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