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
Luba_88 [7]
3 years ago
14

A standard deck of playing cards is shuffled and three people each choose a card. Find the probability that the first two cards

chosen are spades and the third card is red if the cards are chosen with replacement, and if the cards are chosen without replacement. (a) The cards are chosen with replacement. (b) The cards are chosen without replacement.
Mathematics
1 answer:
Andru [333]3 years ago
7 0

Answer:

Part (a) The cards are chosen with replacement is 0.03125 or 1/32

Part (b) The cards are chosen without replacement is 0.0306 or 13/425.

Step-by-step explanation:

Consider the provided information.

A standard deck of playing cards is shuffled 3 cards are chosen.

In a deck of card 13 are spade out of 52 cards. 26 cards are red out of 52 cards.

We need to find the probability that the first two cards chosen are spades and the third card is red.

Part (a) The cards are chosen with replacement.

Suppose the first card is spade then the probability is P(A) = 13/52

As spade are 13 out of 52.

Now, the card is replaced back in the deck and we again draw a card. The probability of getting spade in second time is P(B) = 13/52.

The card is replaced back in the deck and we again draw a card. The probability of getting a red card in third time is P(C) = 26/52.

Now Multiply 3 fraction together as shown.

P(A)\times P(B) \times P(C) =\frac{13}{52} \times \frac{13}{52} \times \frac{26}{52}\\P(A)\times P(B) \times P(C) =\frac{1}{4}\times \frac{1}{4}\times \frac{1}{2}\\P(A)\times P(B) \times P(C) =\frac{1}{32}=0.03125

Hence, the probability of getting the first two cards chosen are spades and the third card is red if the cards are chosen with replacement is 0.03125 or 1/32.

Part (b) The cards are chosen without replacement.

Suppose the first card is spade then the probability is P(A) = 13/52

Now, the card is not replaced back in the deck and we again draw a card. The probability of getting spade in second time is P(B) = 12/51.

The probability of getting a red card in third time is P(C) = 26/50.

Now Multiply 3 fraction together as shown.

P(A)\times P(B) \times P(C) =\frac{13}{52} \times \frac{12}{51} \times \frac{26}{50}\\P(A)\times P(B) \times P(C) =\frac{13}{425}=0.0306

Hence, the probability of getting the first tow cards chosen are spades and the third card is red if the cards are chosen without replacement is 0.0306 or 13/425.

You might be interested in
Joshua has $560. He wants to buy a laptop that costs $320 as well as a case for the laptop that costs $65 and is currently on sa
Igoryamba

Answer:$154.73

Step-by-step explanation:

Take 65 and multiple .15 and that will give you the 15% off of the case. When u do that you get 9.75 so then 65-9.75= 55.25 multiply .08 for the sales tax on the case = 4.42 add to 55.25= 59.67 then add the sales tax for the laptop 320 multiplied by .08 = 25. 60 for a total of 345.60 then add that to 59.67 = 405.27 then u have to subtract that from 560 and Josh has $154.73

6 0
3 years ago
What is the surface area for this?
IrinaK [193]

Answer:

143 cm²

Step-by-step explanation:

There are 3 pairs of sides to this shape,

1 pair is the top and bottom pieces, each has an area of 4(3) = 12 cm², so there are 24 cm² from this pair.

the second pair is the front and back pieces, each has an area of

4(8.5) = 34 cm², so there are 68 cm² from this pair.

the third pair are the side pieces, each has an area of

3(8.5) = 25.5 cm², so there are 51 cm² from this pair.

Al together there are 24 + 68 + 51 = 143 cm²

4 0
3 years ago
In need help quick and can you also explain how you did or what I'm supposed to be doing
Harman [31]
-45x+72
you multiply the 9 by everything in the parentheses
3 0
3 years ago
Read 2 more answers
How does a "for every" statement show a ratio comparison?
Alchen [17]
Example: For every 3 boys, there are 4 girls.

Ratio: 3:4 also 3/4

How to use it?

Example question: If there are 3 boys for every 4 girls and there are 27 boys in the class, how many girls are there?

How to set up the ratio:

3 27
— = —
4 x


Solve it?

[Cross Multiply]

3x= 108

[Divide]

X= 36

How to check it?

Reduce 27/36 and see if it equals 3/4

OR

Plug both into the calculator and both should come out with the same decimal. In this case it is 0.75
8 0
3 years ago
Could someone help me please!! I'm not getting any of the answers! (Math)
ruslelena [56]
3x + y = 3
x + y = 2

x = 1/2 and y = 3/2
8 0
2 years ago
Other questions:
  • Help<br> the question is in the pic below
    12·1 answer
  • The function g is defined by g(x)=ax−7, where a is a constant. Find a, if the graph of g passes through the point ( 1/3,−2).
    13·1 answer
  • In the triangles, TR= GE and SR=FE. If GF= 3.2 ft, which is a possible measure of TS?
    11·2 answers
  • TRIGONOMETRY ANSWER FAST PLS!!!
    10·1 answer
  • Peter ran 15 miles without stopping during the marathon. Anne ran the distance that 1/3 Peter ran before she stopped.
    9·1 answer
  • Danielle wants to know if a new dresser will fit next to her bed. The dresser she would like to buy is 73 centimeters wide. She
    13·1 answer
  • !!!!!!Please help !!!!!!
    8·2 answers
  • E help mah brotha pls
    13·2 answers
  • I need help explaining this please .
    6·1 answer
  • Given: AD = BC and AD || BC<br> Prove: ABCD is a parallelogram.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!