1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
anygoal [31]
3 years ago
14

Pick two cards at random from a well-shuffled deck of 52 cards (pick them simultaneously so they are not the same card). There a

re 12 cards considered face cards. There are 4 cards with the value 10. Let X be the number of face cards in your hand. Let Y be the number of 10's in your hand. Explain why X and Y are dependent.
Mathematics
1 answer:
Scrat [10]3 years ago
7 0

Answer:

The variables X and Y are dependent.

Step-by-step explanation:

The variable <em>X</em> denotes number of face cards . That is it can take values,

<em>X</em> = {0, 1, 2 }

Compute the probability for all he values of <em>X</em> as follows:

P [X = 0] = P (None of the 12 card is chosen in either draw)

              = (40/52)×(39/51)

              = 1560/2652

              = 0.5882

P [X = 1] = P (One of the card is face card is selected)

              = 2×(40/52)×(12/51)

              = 960/2652

              = 0.3619

P [X = 2] = P (Two of the 12 card is chosen in the draw)

              = (12/52)×(11/51)

              = 132/2652

              = 0.0498

The variable <em>Y</em> denotes number of cards numbered 10 . Thus, it can take values:

<em>Y</em> = {0, 1, 2 }

P [Y = 0] = P (None of the 4 card is chosen in either draw)

              = (48/52)×(47/51)

              = 2256/2652

              = 0.8507

P [Y = 1] = P (One of the 4 card is chosen in either draw)

              = 2×(4/52)×(48/51)

              = 384/2652

              = 0.1448

P [Y = 2] = P (Two of the 4 card is chosen in the draw)

              = (4/52)×(3/51)

              = 12/2652

              = 0.0045

Now compute the probability of (<em>X</em> and <em>Y</em>).

P [X = 0 and Y = 0] = P(None of the 16 card is chosen in either draw)

                              = (36/52)×(35/51)

                              = 1260/2652

                              = 0.4751

The variables <em>X</em> and <em>Y</em> are independent if,

P [X = 0 and Y = 0]  = P [X = 0] × P [Y = 0]

                               =  P [X = 0] × P [Y = 0]

                               = 0.8507 × 0.5882

                               = 0.5204

The two values are not equal.

Hence, the variables X and Y are not independent.

You might be interested in
This diagram of airport runway intersections shows two parallel runways. A taxiway crosses both runways. How are 6 and 2 related
miskamm [114]
I need help with this too haha I can't find it anywhere
4 0
2 years ago
Read 2 more answers
What is the measure of the larger angle in this degree?​
Pie
Answer:

A straight line is equivalent to 180 degrees with that in mind,

(2.4x)+(9.6x)=180
2.4x+9.6x=180
12x=180
12x/12=180/12
x=15

Now to find the measurement of the larger angle,

9.6*15=144
Just in case you need it
180-144=36
Which is your smaller measurement.
5 0
3 years ago
The width x of your iris decreases from 4 millimeters to 2 millimeters when you enter a dark room. How many times greater is the
inysia [295]

Answer:

The area of the Iris is 4 times greater.

Step-by-step explanation:

Firstly, we have to realize that we cannot solve this problem without knowing the radius of the iris. because from the information given, the radius of the iris could well be the size of the galaxy and contract from width of 4mm to 2mm and we wouldn't know!

The average radius of the iris is 6mm, so we take this value.

Now, initially the width of the iris is 4mm, that means the radius of the pupil is:

6mm-4mm=2mm

Therefore it's area A is:

A=\pi r^2=\pi (2)^2=4\pi

When the iris contracts to 2mm, the radius of the pupil becomes:

6mm-2mm=4mm

Then it's area is A:

A=\pi r^2=\pi (4)^2=16\pi

To find how many times greater this final area is than the initial area, we just divide it by the initial area:

\frac{16\pi }{4\pi } =4

This is 4 times greater than the initial area.

3 0
3 years ago
What does the expression ∙ represent?
nirvana33 [79]
I think you are missing something, what expression?

If you mean the • dot, it means multiplication.
3 0
2 years ago
Read 2 more answers
Sarah needs 10 feet of fabric for a project she is working on, but the store only sells the fabric in meters. One meter of fabri
Aleks [24]
<h2>Hello!</h2>

The answer is:

The fabric will cost $4.58

D.$4.58

<h2>Why?</h2>

Since it's a conversion exercise, we need to pay special attention to the conversion procedure.

From the statement we know that:

1ft=0.305m

So, if she needs 10 feet of fabric, we need to convert it to meters, and then, calculate its cost.

We have that:

10*1ft=10*0.305m\\\\10ft=3.05m

Now, we have that each meter of fabric cost $1.50, so, 3.05m of fabric will cost:

\frac{1m}{1.50(dollars)}=\frac{3.05m}{cost}\\\\cost=\frac{3.05m*1.50(dollars)}{1m}=4.575(dollars)=4.58(dollars)

Hence, we have that the cost of the fabric will be $4.58.

The correct option is: D.$4.58​

Have a nice day!

6 0
2 years ago
Other questions:
  • Let θ be an angle in quadrant III such csc(θ)=-(13)/(5). . Find the exact values of tan θ and cosθ ?
    10·1 answer
  • (Extra points)
    9·1 answer
  • -|36| + | 7 | = what is the value
    14·2 answers
  • Ellie uses 27 feet of fabric to make 48 doll dresses.she uses the same amount of fabric to make each dress.how many yards of fab
    13·2 answers
  • Before reporting the results of the survival analysis, the investigators compared baseline characteristics of the 38 people who
    9·1 answer
  • Use the number line below, where RS = 6y + 3, ST = 4y + 7, and RT = 60.​
    14·2 answers
  • Help asap??!!?!?!.....................................!
    6·1 answer
  • Simplify<br> 5 x 52<br> leaving your answer in index form.
    7·2 answers
  • Given the arithmetic sequence where an= 3 + 2(n-1), what is the domain for n?<br>​
    7·1 answer
  • Question Solve. 2 1/3−1/2x=−2/3 Enter your answer in the box.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!