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
Help me im tired of posting
yaroslaw [1]

Stop posting this. It's very rude to continue posting this. One post was enough.

8 0
2 years ago
Read 2 more answers
What is a quadratic function in standard form given the roots -4 and -1
AlexFokin [52]

Step-by-step explanation:

a=-4

a=-2

(a-(-4)(a-2)

(a+4)(a-2)

aa-2a+4a-8

a2-2a-8

6 0
3 years ago
Any one help please
zvonat [6]

Answer:

1: male + female \leq 30

2: 140 + 25x \geq 550

Step-by-step explanation:

8 0
3 years ago
I need help please and thank u,
Alchen [17]

The illegal values of b are when the denominator equals 0.

So, b^2-2b-8=0 gives you (b-4)(b+2)=0

Therefore, b=4 and b=-2, which is answer A.


8 0
3 years ago
A sphere has a radius of 12 inches. A second sphere has a radius of 9 inches. What is the difference of the volumes of the spher
just olya [345]

Answer:

Solution given;

for sphere

radius [r]:12inches

another

radius [R]:9inches

Now

difference in volume of sphere:

volume of sphere of having radius [r-R]

=\frac{4}{3} πr³-\frac{4}{3} πR³

=\frac{4}{3} π(12³-9³)

= 1332π cubic inches

The volume of the larger sphere is <u>___1332</u>__π cubic inches greater than the volume of the smaller sphere.

3 0
3 years ago
Other questions:
  • Which choice shows a 90 degree clock wise rotation of the figure about point p
    10·1 answer
  • oceanside bike rental shop charges a $17 fixed fee plus six dollars an hour for renting a bike. Tim paid $47 to rent a bike. How
    11·1 answer
  • What is 100 • 100, using standard multiplication?
    9·2 answers
  • An amusement park's owners are considering extending the weeks of the year that it is opened. The owners would like to survey 10
    9·2 answers
  • 2. -3xy, when x = 4 and y = 2​
    15·1 answer
  • How many tens arein 290
    10·1 answer
  • Help! :') ..........................................​
    11·2 answers
  • can someone write a paragraph explaining in your own words how muscles and bones work together, PLEASEEEEEEEEEE
    10·1 answer
  • there were 60 people in the town's first annual parade. That number has been growing by about 5% each year. predict the number o
    5·1 answer
  • I need help with number 8
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!