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
Dvinal [7]
2 years ago
10

You have a standard deck of cards. The deck has 52 total cards and contains 4 suits: hearts, clubs, diamonds, and spades. Each s

uit consists of cards numbered 2-10, a jack, a queen, a king, and an ace.
You select one card at random from the deck. Let A be the event that the randomly selected card is a diamond and let B be the event that the card is a king. Based on this information, answer the following questions.

Mathematics
1 answer:
MrRa [10]2 years ago
8 0

Answer:

P(A) = \dfrac{1}{4}\\P(B) = \dfrac{1}{13}\\P(A \cap B) = \dfrac{1}{52}\\P(A/B) = \dfrac{1}{4}\\P(A/B) =  P(A)\\

A and B are not independent events.

Step-by-step explanation:

Total number of possibilities is 52 (Total number of cards in the deck).

Formula for probability of an event <em>E </em>can be observed as:

P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}

For event A, number of cases possible for a card to be diamond = 13

P(A) = \dfrac{13}{52} \\\Rightarrow P(A) = \dfrac{1}{4}

For event B, number of cases possible for a card to be a king = 4

P(B) = \dfrac{4}{52} \\\Rightarrow P(B) = \dfrac{1}{13}

For the event, A \cap B, the card is a king and diamond, only one case is possible.

Because there is only one card for king of diamond.

P(A \cap B) = \dfrac{1}{52}

Formula for P(A/B):

P(A/B) = \dfrac{P(A \cap B)}{P(B)}

\Rightarrow \dfrac{\dfrac{1}{52}}{\dfrac{1}{13}}\\\Rightarrow \dfrac{1}{4}

Yes, P(A) is same as P(A/B).

Here, A and B are not independent events because they have a common case i.e. a <em>king </em>is there which is of <em>diamond </em>in the deck.

You might be interested in
868 is greater than or less than 887
jeyben [28]
The answer for this is less than 887
5 0
3 years ago
Read 2 more answers
Graph the image of F(-8, 10) after a rotation 180° counterclockwise around the origin.
pychu [463]

Answer:

F' is at (8, -10)

Step-by-step explanation:

clockwise or counter-clockwise do not matter when the rotation is 180°

6 0
2 years ago
On Tuesday Emily bought four posters,
hram777 [196]

Answer: 16 posters

Step-by-step explanation:

Monday - Had owned 16 posters

Tuesday - Bought 4 posters, adding up to 20

Wednesday - Half of the posters were destroyed, half of 20 is 10

Thursday - 10 posters remained.

8 0
2 years ago
Read 2 more answers
A triangle has sides xcm, (x + 4) cm and 11cm, where x is a whole number of cm. if the perimeter of the triangle is less than 32
NARA [144]

9514 1404 393

Answer:

  {4, 5, 6, 7, 8}

Step-by-step explanation:

The inequality related to the perimeter is ...

  x +(x +4) +11 < 32

  2x < 17 . . . . . . . . . . . . subtract 15

  x < 8.5

The inequality related to the triangle inequality is ...

  (x) +(x +4) > 11

  2x > 7

  x > 3.5

Then possible whole-number values of x are ...

  {4, 5, 6, 7, 8}

6 0
3 years ago
Read 2 more answers
RSM HOMEWORK HELP!!!
Gnesinka [82]

Answer:

Step-by-step explanation:

∠CAB = 33       {alternate interior angles}

5x = 33 + 2x    { exterior angle equals sum of opposite interior angles}

5x - 2x = 33

3x = 33

x = 33/3

x = 11

∠B = 2x = 2* 11 = 22

∠ECB = 5x = 5*11 = 55

8 0
3 years ago
Read 2 more answers
Other questions:
  • A ball is thrown from a height of 43 meters
    14·1 answer
  • The volume of a cone is 3x* cubic units and its height is x units.
    14·1 answer
  • ASAP ANYONE PLEASE tell me if I’m right !
    11·2 answers
  • WHAT TWO NUMBERS MULTIPLY TO 27<br><br> WHAT TWO NUMBERS MULTIPLY TO 18
    9·2 answers
  • Paul has 30$ to spend at the fair if the admission to the fair is 5$ and the rides cost 3.50 each how many rides can paul go on
    11·2 answers
  • I NEEEDDD HELPPP!!! someone please help me outttt
    14·1 answer
  • Which relation is a function of x? ​
    14·1 answer
  • Find the value of x in the triangle.
    8·2 answers
  • In which number is the digit 5 one hundred times larger than it is in the number 253
    10·1 answer
  • Sophia has 8 spend on lunch .Does she have enough money for a sandwich a drink and a bag of chips
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!