] Consider a randomly shuffled deck of ten cards labeled {1, 1, 2, 2, 3, 3, 4, 4, 5, 5}, of which game play requires three to be drawn. Which one should be worth more points: A getting a pair of matching cards within the three, or B getting a set of three cards that can be arranged such that the sum of two of them is the value of the third (e.g. 1 2

Answers

Answer 1

Answer:

B should be worth more points.

Step-by-step explanation:

Given -  Consider a randomly shuffled deck of ten cards labeled

              {1, 1, 2, 2, 3, 3, 4, 4, 5, 5}, of which game play requires three

               to be drawn.

To find - Which one should be worth more points:

              A getting a pair of matching cards within the three,

              or B getting a set of three cards that can be arranged such

              that the sum of two of them is the value of the third.

Proof -

Given that, three cards has to be drawn.

So, total number of ways the card be drawn = ¹⁰C₃

                                                                      = [tex]\frac{10!}{3! (10-3)!}[/tex]

                                                                      = [tex]\frac{10!}{3! 7!}[/tex]

                                                                      = [tex]\frac{10.9.8.7!}{3! 7!}[/tex]

                                                                      = [tex]\frac{10.9.8}{3.2.1}[/tex]

                                                                      = 120

⇒¹⁰C₃ = 120

Now,

Given that, A getting a pair of matching cards within the three

Sample space = { (1,1,2), (1,1,3).(1,1,4),(1,1,5);

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

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

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

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

⇒n(A) = 20

Also,

B getting a set of three cards that can be arranged such that the sum of two of them is the value of the third

Sample space = { (1,1,2),(1,2,3),(1,3,4),(1,4,5),(2,2,4),(2,3,5) }

⇒n(B) = 6

Now,

P(A) = [tex]\frac{20}{120} = \frac{1}{6}[/tex] = 0.167

P(B) = [tex]\frac{6}{120} = \frac{1}{20}[/tex] = 0.05

We can see that, P(B) < P(A)

⇒B should be worth more points.


Related Questions

Divide the given polynomial by the given monomial.​

Answers

Answer:

Looks like all of your questions have been answered.

A hyperbola centered at the origin has a vertex at (3, 0) and a focus of the hyperbola is located at (9,0). What are
the equations of the directrices?
x = +

Answers

Answer:

Step-by-step explanation:

x²/a² - y²/b² = 1

center (0,0)

vertex (3,0), so a = 3

focus (9,0)

e = 9/a = 3

directrices: x = ±a/e = ±1

The equations of the directrices with a vertex at (3, 0) and a focus of the hyperbola located at (9, 0) is x =  ±1.

What is the general equation of hyperbola?

The general equation of the hyperbola is in the form of

x²/a² - y²/b² = 1

We have been given center (0,0)

vertex (3,0),

so a = 3

focus (9,0)

So, e = 9/a = 3

The equation of directrices:

x = ±a/e = ±1

Hence, The equations of the directrices with a vertex at (3, 0) and a focus of the hyperbola located at (9, 0) is x =  ±1.

Learn more about hyperbola here:

brainly.com/question/4148030

#SPJ2

What is (6 x 10) + 9

Answers

Answer:

(60) + 9 = 69

Step-by-step explanation:

HOPE I HELPED, IM NEW

Answer:

Since if you know your multiplication tables 10x6= 60+9=69

Step-by-step explanation:

Answer 69

a) One of two boxes contain 4 red balls and 2 green balls and the second box contains 4 green and two red balls. By design, the probabilities of selecting box 1 or box 2 at random are 1/3 for box 1 and 2/3 for box 2. A box is selected at random and a ball is selected at random from it. a) Given that the ball selected is red, what is the probability it was selected from the first box? b) Given that the ball selected is red, what is the probability it was selected from the second box? c) Compare the results in parts a) and b) and explain the answer.

Answers

Answer:

The answer is below

Step-by-step explanation:

Let B₁ represent box 1, B₂ represent box 2, E₁ represent the event of selecting box 1, E₂ represent the event of selecting box 2 and R represent the event of selecting a red ball.

Given that:

Probability of selecting box 2 P(E₂) = 2/3, Probability of selecting box 1 = P(E₁) = 1/3

Probability of selecting red ball from box 1 = P(R | E₁) = 4/6 [4 red balls out of 4 red, 2 green]

Probability of selecting red ball from box 2 = P(R | E₂) = 2/6 [2 red balls out of 2 red, 4 green]

a)

Given the ball is red, the probability it was selected from the first box is:

[tex]P(E_1|R)=\frac{P(R|E_1)P(E_1)}{P(R|E_1)P(E_1)+P(R|E_2)P(E_2)} =\frac{2/3*1/3}{(2/3*1/3)+(1/3*2/3))} =\frac{1}{2}[/tex]

b)

Given the ball is red, the probability it was selected from the second box is:

[tex]P(E_2|R)=\frac{P(R|E_2)P(E_1)}{P(R|E_2)P(E_2)+P(R|E_1)P(E_1)} =\frac{1/3*2/3}{(1/3*2/3)+(2/3*1/3))} =\frac{1}{2}[/tex]

c)

We can see that both probabilities are equal. Although we have more red balls in box 1 (twice as much) than in box 2 but the probability of selecting from box 2 (is twice as much) than from selecting from box 1.

The probability that the ball selected is red and it is selected from the first box is 1/2 and the probability that the ball selected is red and it is selected from the second box is 1/2.

Given :

One of the two boxes contains 4 red balls and 2 green balls and the second box contains 4 green and two red balls. By design, the probabilities of selecting box 1 or box 2 at random are 1/3 for box 1 and 2/3 for box 2.

a) The probability that the ball selected is red and it is selected from the first box is:

[tex]P(E_1|R)=\dfrac{P(R|E_1)P(E_1)}{P(R|E_1)P(E_1)+P(R|E_2)P(E_2)}[/tex]

[tex]P(E_1|R)=\dfrac{\dfrac{2}{3}\times \dfrac{1}{3}}{\dfrac{2}{3}\times \dfrac{1}{3}+\dfrac{1}{3}\times \dfrac{2}{3}}[/tex]

[tex]P(E_1|R)=\dfrac{1}{2}[/tex]

b) The probability that the ball selected is red and it is selected from the second box is:

[tex]P(E_2|R)=\dfrac{P(R|E_2)P(E_2)}{P(R|E_1)P(E_1)+P(R|E_2)P(E_2)}[/tex]

[tex]P(E_2|R)=\dfrac{\dfrac{2}{3}\times \dfrac{1}{3}}{\dfrac{2}{3}\times \dfrac{1}{3}+\dfrac{1}{3}\times \dfrac{2}{3}}[/tex]

[tex]P(E_2|R)=\dfrac{1}{2}[/tex]

c) The probability that the ball selected is red and it is selected from the first box and the probability that the ball selected is red and it is selected from the second box is the same.

For more information, refer to the link given below:

https://brainly.com/question/795909

What is the slope of line m?
On a coordinate plane, a straight line goes through (negative 2, 1), (0, 0), and (2, negative 1).

Answers

Given:

A straight line goes through (-2,1), (0,0), and (2,-1).

To find:

The slope of the given line.

Solution:

Slope formula

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Consider any two points from the given points.

The line goes through (-2,1) and (0,0). So, the slope of the line is

[tex]m=\dfrac{0-1}{0-(-2)}[/tex]

[tex]m=\dfrac{-1}{2}[/tex]

Therefore, the slope of the line is [tex]m=-\dfrac{1}{2}[/tex].

Answer:

its 2/3

Step-by-step explanation:

provided
What is the value of 2 in the equation 60x = 360x

Answers

It would be 6 I hope I helped

Ellen ordered some books online. Each book cost $13 and there is a $20 shipping fee.
Which expression represents the situation?
A 7n
B) 13n + 20
C) 33n
D) 20n + 13

Answers

Answer:

Step-by-step explanation:

the correct expression is B

13*n+20

where n represents the number of the books

Please help it’s for homework

Answers

Slope is 5
Y intercept is -8
y = 5x - 8
The answer should be y=5x-8

Which region indicates the intersection of the system 2x + 3y > 3 and y sx - 1?

Answers

Answer:

I think Region 1 is my answer, because the first equation is -1.1 and thats the closest point

he FDAL level for insect filth in chocolate is 0.6 insect fragments (larvae, eggs, body parts, and so on) per grams. Suppose that there is an average of 0.57 insect fragments per gram of chocolate bar and the distribution is following a Poisson distribution. Compute the probabilities that the number of insect fragments in a 50-gram sample of chocolate bar are:

Answers

Answer:

Step-by-step explanation:

[tex]\text{To find :} \\ \\ 1.) \ \ \text{More than 20} \\ \\ 2) \text{Less than 30 } \\ \\ 3) \ \text{Within the range of }( \mu - \sigma , \mu +\sigma)[/tex]

[tex]\ \ \ Since \ \ X \ \text{follows a poisson distribution and;} \\ \\ X\sim Poisson (0.57) per \ gram \\ \\ X \sim Poisson (28.5) \ per \ 50 \ grams \\ \\[/tex]

[tex]1) \ \ \ \text{The probability } P(X>20) = \sum \limits ^{50}_{x=21} \dfrac{e^{-28.5}\times 28.5^x}{x!} \\ \\ \mathbf{ = 0.9389}[/tex]

[tex]2) P( X<30) = \sum \limits ^{29}_{x=0} \dfrac{e^{-28.5}\times 28.5^x}{x!} \\ \\ \mathbf{=0.5861}[/tex]

[tex]\text{3) Since then mean}\ \mu = 28.5 \\ \\ \sigma =\sqrt{28.5} = 5.339 \\ \\ \mu - \sigma = 28.5 -5.339= 23.161 \\ \\ \mu + \sigma = 28.5 + 5.339 = 33.839[/tex]

[tex]P(23.161 < X< 33.839) = \sum \limits ^{33}_{24} \dfrac{e^{-28.5}\times 28.5^x}{x! } \\ \\ = P(X\le 33) - P( X \le 23) \\ \\ = 0.82678 - 0.1750 \\ \\ \mathbf{= 0.6516}[/tex]

Six more than five times a number

Answers

Answer:

? = 5n + 6

Explanation:

Answer:

5x + 6

Step-by-step explanation:

Let the number = x. 5 times x = 5x. So, the equation 5x + 6.

Consider the figure shown below. What is the value of the angle x?

x = _______ degree. ​

Answers

X=66 degrees. Because of corresponding alternate interior angles. Interior angles of triangle is 180 degrees

Find the slope of the line containing the given pair of points. If the slope is​ undefined, state this. (-8,0) and (4,0)

Answers

Answer:

The slope is 0

Step-by-step explanation:

Given

[tex](x_1,y_1) = (-8,0)[/tex]

[tex](x_2,y_2) = (4,0)[/tex]

Required

The slope (m)

This is calculated as"

[tex]m=\frac{y_2-y_1}{x_2 - x_1}[/tex]

[tex]m=\frac{0-0}{4 -(-8)}[/tex]

[tex]m=0[/tex]

The slope is 0

Solve for x: 8x = 2/3
solve for x: 1/4x =5​
two questions

Answers

Answer: x=5

x= 2

Step-by-step explanation:

Multiply and then simplify completely: ( 8 + √ 10 ) ( 8 − √ 10 )

Answers

Answer:

54.

Step-by-step explanation:

( 8 + √ 10 ) ( 8 − √10)

= 8*8  - 8√10 + 8√10  +√10 *  -√10

= 64 -  8√10 + 8√10 - 10

The 2 middle turns cancel out so we have:

64 - 10

= 54.

Directions: Solve for x. Round to the nearest tenth
1.
х
63°
16

Answers

Okay so we are going to use Cos for this equation since this is Adjacent/hypotenuse.

I am going to attach a picture for the steps.

x=7.26

Answer all of these please

1.The product of a number and seven more than the number

2.The product of a number and seven less than the number

3.Eight less than twice a number is fourteen.

4.One less than three times a number is seven.

5. Four more than five times a number is two less than the number.

6.Ten less than a number is three more than six times the number.

7.Twice the sum of a number and 3 is 20.

Answers

Answer: 3. 22-8 / 4. 2x3.5 / 5.

Step-by-step explanation:

Step-by-step explanation:

1. 1×8=8

2. 9×2=18

3. 8+14=22÷2=11

4. 2.7

5. -1.5

6. closest -2.5

7.÷2=10-3=7

Please guys, can someone help me out?

Answers

Center point= 8 , 3
radius =7 Good luck!

WILL GIVE BRAINLIEST
If there are 2 boys and 3 girls in a group. What is the ratio of girls to boys? Express the ratio in 3 different ways. ( Place commas in between each way )

Answers

Answer:

2 to 3, 4 to 6, 8 to twelve

Step-by-step explanation:

the boys are first, girls second

Answer: 3:2 ... 9:6... 27:18 you can put 81:54 too

Step-by-step explanation:

Please help!! Needed ASAP!!

Answers

Answer and Explanation:

If, on the other hand, the graph "flexes" or "flattens out" to some degree when it goes to cross the axis, then the zero is of a higher multiplicity; that is, it'll be of multiplicity three, five, or higher.

When a graph doesn't start at 0, it means that the graphs before it is not shown.

For number 4, I'd suggest Graph 3.

For number 3, I'd suggest graph 1.

For number 5, Write something along the lines of "Graph 2 does not show the car stopping slowly, it stops suddenly. Then it starts going really fast and stops suddenly again."

I hoped this helped.

Containers A (6cm, 5cm, 4cm), B (5cm, 4cm, 3 cm) and C (3cm, 3cm, 2 cm) are three rectangular containers. At first, container A is filled with water to its brim while containers B and C are empty. Next, some water from container A is poured into containers B and C so that container B is completely full while container C is half full. Find the height of the water left in container A...

Answers

Answer:

Step-by-step explanation:

From the given equation
a) Copy and complete the table
b) Draw the graph of the given equation
c) Find the coordinates of y-intercep

Answers

Answer:

See attached

a)

The table:

x | -3 | -2 | -1 | 0 | 1  | 2 | 3y | -5 | -3 | -1 | 1  | 3 | 5 | 7

b)

The graph is pictured

c)

The y-intercept has coordinates of (0, 1)

5 books cost $15. How much do 7 books cost?

Answers

5 / 15 = 3

So 3 x 7 = 21
ANSWER:
$21

STEP BY STEP:
Each book is 3 dollars, so we multiply 7 by 3, and you get 21.

hope this helps

Story Problem:
Avery purchased 4 tacos and 2 burritos and her total cost was $21. Sasha purchased 4 tacos and 3 burritos
and her total cost was $26.50. What is the price of one burrito?

Answers

Answer:

Step-by-step explanation:

Let tacos be x and burritos be y

So, Avery purchased 4x+2y = 21

Sasha purchased 4x+3y = 26.5

Solving the 2 eqns:

4x+2y=21

-4x-3y=-26.5

-y=-5.5

The cost of one burrito is $5.5

(X+15)+(x+5)+(x+15)+(X+5)

Answers

Answer:

4 + 4 0

Step-by-step explanation:

Simplify

1

Eliminate redundant parentheses

( + 1 5 ) + ( + 5 ) + ( + 1 5 ) + ( + 5 )

2

Add the numbers

3

Combine like terms

Solution

4 + 4 0

Which of the following are compound events in which the results of one event affect the likelihood of the other event? PLZ HELP ASAP
Answers: 1. independent events
2. dependent events
3. theoretical events
4. fair events

Answers

Answer:

2. Dependent events

Step-by-step explanation:

How many samples of size 2 can be formed from population of size 5

Answers

Answer:

2

Step-by-step explanation:

At the We-Pack Shipping, the workers can unload 28 trucks in 7 hours. Which of the following is a correct unit rate for this situation?

1 truck per hour
4 hours per truck
1 over 4. of a truck per hour
1 over 4. of an hour per truck

Answers

Answer:

4 trucks per hour

Step-by-step explanation:

You would do the trucks over the hours to get the ratio so, 28:7 is equal to 4:1 because 28/7 = 4

4 trucks per hour? Maybe the last one I’m not sure the question isn’t very clear

Red gold has 3 parts gold and one part copper how much carat gold it will be

Answers

Answer: 0.75 ×24 carat = 18 carat

Step-by-step explanation:

24 carat is 100% pure gold. If there is 3/4 parts of gold it is 75 % = 0.75

I have a cage with cats and birds. there are 12 heads and 32 feet. how many
birds are there

Answers

12x4=48

48-32=16

4-2=2

16 divided by 2=8 birds

Answer:

4 cats, 8 birds

Step-by-step explanation:

make a system of equations and solve.

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