Two dice are rolled. A = ‘sum of two dice equals 3’ B=‘sumoftwodiceequals7’ C=‘at
least one of the dice shows a 1’ (a) What is P (A|C)?
(b) What is P (B|C)?
(c) Are A and C independent? What about B and C?

Answers

Answer 1

Presumably, the two dice are fair, so that each face has an equal 1/6 probability of being rolled. We roll 2 dice, so there are 6² = 36 possible outcomes, each with 1/36 probability of occurring.

We have

• P(A) = 2/36 = 1/18, because there are only 2 ways to roll a sum of 3 (1+2 and 2+1)

• P(B) = 6/36 = 1/6, because there are 6 ways of rolling a sum of 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1)

• P(C) = 12/36 = 1/3, because if 1 die shows a 1, then there are 6 possible values for the other die, and vice versa)

(a) By definition of conditional probability,

P(A | C) = P(A and C) / P(C)

A and C only occur together if we had rolled either {1, 2} or {2, 1}, so ultimately

P(A and C) = P(A)

so that

P(A | C) = (1/18) / (1/3) = 3/18 = 1/6

(b) From the definition,

P(B | C) = P(B and C) / P(C)

By the same reasoning as in (a), we have to roll either {1, 6} or {6, 1} to have both B and C occur, so

P(B and C) = (2/36) / (1/3) = 6/36 = 1/6

(c) In order for two events X and Y to be independent, we need to have

P(X and Y) = P(X) P(Y)

or in terms of conditional probability,

P(X | Y) = P(X and Y) / P(Y) = P(X) P(Y) / P(Y) = P(X)

Then it follows that A and C are not independent, while B and C are independent.


Related Questions

if (x+30°) and (180°-2x) are vertically opposite angles . Find the value of x .​

Answers

Answer:

50

Step-by-step explanation:

x + 30 = 180 - 2x   [vertically opposite angles]

x = 180 - 30 - 2x

x = 150 - 2x

x + 2x = 150

3x = 150

x = 150/3

x = 50

dentify the error in finding the distance between A(6,2) and B(1,−4).

Answers

The answer I think is A

PLEASE HELP! it's due today

Answers

Answer:

[tex]thank \: you[/tex]

Whats the answer and the steps
2(3x-4)

Answers

Answer:

-24

Step-by-step explanation:

2(3x-4)

6x-8

where does 0.5 goes on a real number line​

Answers

5 points after 0, and in between 0 and 1 in the middle

write each expression as a single power of 10

Answers

Answer:

[tex]{ \underline{ \sf{it \: is \: {10}^{9} }}}[/tex]

Step-by-step explanation:

[tex](10 {}^{4} ). \frac{ {10}^{12} }{ {10}^{7} } = ( {10}^{4} ). {10}^{(12 - 7)} \\ \\ = ( {10}^{4} ). {10}^{5} \\ = {10}^{(4 + 5)} \\ = {10}^{9} [/tex]

Answer:

[tex]10^{9}[/tex]

Step-by-step explanation:

I. [tex]10^{4} * 10^{12-7}[/tex]

= [tex]10^{4} * 10^{5}[/tex]

= [tex]10^{4 + 5}[/tex]

= [tex]10^{9}[/tex]

Find the perimeter, in units, of the polygon with the given vertices. Plot the points.
Round to the nearest tenth.
5. A(8,0), B(-3, 2), C(10, 2)
6. A(4, -3), B(7, 10), C(-8, 2)
7. A(-5,5), B(5, -5), C(-5, -5)
8. A(4, -3), B(7,10), C(-8, 2), D(-1, -5)
9. A(-4, -8), B(4, -8), C(4, 0), D(0, 3), E(-4, 0)

Answers

Answer: 9

Step-by-step explanation:

Plot the points

Find the distance of each side

add the three numbers

9

Answer:

5. 27

6. 43

7. 47

Step-by-step explanation:

measure at least pairs of corresponding angles in XJYN and ZSCH using a protractor. Record your measurements to the nearest 5. what do you notice?

Answers

Answer:

any file to have a reference?

Use the distributive property to write an equivalent expression.
8(3v+3w-2)

Answers

24v+24w-16
I multiplied all the numbers inside the parenthesis to 8, so (8 x 3w),(8 x 3v),(8 x -2). Basically Distrbutive property is you distribute the 8 into the numbers inside the parenthesis and by distribute you just multiply. Lemme know if this is the answer you were looking for!

Answer:

8(3v+3w-2)=(8×3v+8×3w-8×2)

Step-by-step explanation:

8×3v=24v.

8×3w=24w. [24v+24w-16]=(8×3v+8×3w-2×8)

8×(-2)=-16.


A group of 20 people are going to run a race. The top 6 finishers advance to the finals. In how many different ways can they advance?

Answers

167960 is your awnser

-6, 20, 4.3, 159/-9
Order from least to greatest

Answers

159/-9, -6, 4.3, 20

what is 2x-9=5x+12 with the step by step

Answers

Answer:

x = -7

Step-by-step explanation:

Please view the detailed answer in the image attached

Answer:

[tex]2x - 9 = 5x + 12 \\ - 3x = 21 \\ x = - 7[/tex]

Step-by-step explanation:

x = -7

Find the equation of the line that contains the point (1,-5) and has a slope that is undefined. Express the equation using either the general form or the slope-intercept form of the equation of a line.
The equation of the line is

Answers

Answer:

x=1

Step-by-step explanation:

Since the slope is undefined, it's of the form x=a and since it passes through (1,-5) the equation is x=1

The equation of the vertical line in slope-intercept form is: x = 1.

What is the Equation of a Vertical Line?

A vertical line has an undefined slope and therefore has no y-intercept. the equation of a vertical line is therefore expressed as, x = a, where a is the x-intercept, which is the value of x of the point where the vertical line intersects the x-axis..

Given the point (1, -5), since the line has an undefined slope, the equation in slope-intercept form would be: x = 1.

Learn more about equation of a vertical line on:

https://brainly.com/question/9050446

#SPJ6

-8=x+ll/-2 solve for x step by step and answer

Answers

Answer:

x=(-5)/2

Step-by-step explanation:

-8×(-2)=-2x+11

16-11=(-2x)

x=(-5)/2

A sum of Rs 105 is divided into two parts.if two times the greater part is 15 less than three times the smaller part, find the parts of the sum.​

Answers

Answer:

Step-by-step explanation:

Let the greater part = x

Smaller part = 105 - x

2*(greater part) = (3*smaller part) - 15

2*x = 3*(105 -x) - 15

Use distributive property

2x = 3*105 - 3*x - 15    

2x = 315 - 3x - 15

2x =  300 - 3x

Add 3x to both sides

2x +3x = 300

5x = 300

Divide both sides by 5

x = 300/5

x =60

Smaller part = 105 - 60  = 45

Greater part = Rs. 60

Smaller part = Rs. 45

Robert wants to buy a digital piano at a yard sale. He makes a scale drawing of his living room. He uses a scale of 1cm in the drawing to 6 inches in the actual room. The width of the digital piano is 54 inches will it fit along the wal. Next to the bookshelf ?

Answers

Answer:

It’s 48 just do 8*6=48 I don’t know how I got that answer but Ik it’s right lol

Jonathon can jog 2 2/7 miles in 2/8 hour. Find his average speed of miles per hour.

Answers

Answer:

9.14 miles an hour

Step-by-step explanation:


What is the answer ?

Answers

Answer:

70 seconds

Step-by-step explanation:

first we'll divide seconds by shirts 28/2 to find out how long it takes to do one shirt. it takes Jonah 14 seconds to do 1 shirt so we can then multiply that by 5 shirts to get 70 seconds

Compare and order the numbers below from least to greatest.
4.6, 2.8, V7, V17,

Answers

Answer:

2.8, 4.6, V7, V17

i hope it help n im sorry i can't explain

Lauren bought snacks for her team's practice. She bought a bag of popcorn for $2.37 and a 6-pack of juice bottles. The total cost before tax was $15.45. How much was each bottle of juice?

Answers

Answer:

$2.18

$15.45-$2.37=$13.08

$13.08/6

$2.18

Which expression has a value of 48?


A . (16−8)×(2+4)

B . 16−(8×2+4)

C . 16−8×(2+4)

D . (16−8)×2+4

Answers

Step-by-step explanation:

(16-8)x(2+4)

= 8x(6)

= 8x6

= 48

PLEASE HELP FAST!! I CANNOT GET THIS WRONG!!!!
Makayla and David work at a furniture store. Makayla is paid $230 per week plus 7.5% of her total sales in dollars, x, which can be represented by g(x)=230+0.075x. David is paid $321 per week plus 4% of his total sales in dollars, x, which can be represented by f(x)=321+0.04x. Determine the value of x, in dollars, that will make their weekly pay the same.

Answers

Answer:

6

Step-by-step explanation:

you kna mean?

What is 10% of a number whose square
is 81

Answers

Answer: 0.9

Step-by-step explanation:

Let x be the number

Determine the value of the number

x² = 81

√x² = √81

x = 9

Find the 10% of the number

Final number = rate of percentage × original number

Final number = 10% × 9

Final number = [tex]\boxed{0.9}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Please help me I’ll give a brainliest! Even if you are only able to do one of them it help because I don’t understand how to do it!!!

Answers

Answer:

The x which is not in the domain of the function is the root of the denominator

6) x+3=0, x=-3 is the x which is not in the domain of the function

7) |2x+5|=0, x=-5/2 is the x which is not in the domain of the function

8) x^2-16=0, x=±4 are the x which are not in the domain of the function

Factoring binomials with the difference of squares

Answers

Answer:

Step-by-step explanation:

y-3 = 2(x+1)
fiind the missing value ?

Answers

Step by step process:

Let's solve for x.

y−3=2(x+1)

Step 1: Flip the equation.

2x+2=y−3

Step 2: Add -2 to both sides.

2x+2+−2=y−3+−2

2x=y−5

Step 3: Divide both sides by 2.

2x/2=y−5/2

x=1/2y+(−5/2)

Answer: x=1/2y+(−5/2)

Let's solve for y.

y−3=2(x+1)

Step 1: Add 3 to both sides.

y−3+3=2x+2+3

y=2x+5

Answer:

y=2x+5

Write a proof. Given x - 2 = 3(x - 4) Prove x = 5

Answers

x=5

Step-by-step explanation:

x-2=3(x-4)

x-2=3x-12

12-2=3x-x

10=2x

x=10/2

x=5

Answer:

x = 5

Step-by-step explanation:

x - 2 = 3(x - 4)

x - 2 = 3x - 12

-2x - 2 = -12

-2x = -10

x = 5

put the following equation of a line into slope intercept form simplifying all fractions 5x + 2y = -6 ​

Answers

Answer:

The general equation of a slope-intercept form is as below;

[tex]y = mx + c[/tex]

m » slope / gradient

c » y - intercept

x » x - intercept

Since our equation is 5x + 2y = -6, make y the subject:

[tex]5x + 2y = - 6 [/tex]

subtract 5x from either sides:

[tex](5x + 2y) - 5x = - 6 - 5x \\ 2y = - 5x - 6[/tex]

apply the division rule of equality:

[tex] \frac{2y}{2} = \frac{ - 5x}{2} - \frac{6}{2} \\ \\ { \boxed{ \boxed{answer : \: y = - \frac{5}{2} x - 3}}}[/tex]

slope » -5/2

y - intetcept » -3

HELPPPPPP MEEEE PLESDEEEE

Answers

Answer:

7, 5, 1, 3

Step-by-step explanation:

Hope this Helps!

Please mark me Brainliest

Which variable is dependent temperature or time of day? Which variable is independent?​

Answers

Answer:

 The temperature depends on the time.

The independent variable is the variable the experimenter manipulates or changes.

Hope it helps you.
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