MATHEMATICS COLLEGE

A deck of cards contains 52 cards. They are divided into four suits: spades, diamonds, clubs and hearts. Each suit has 13 cards: ace through 10, and three picture cards: Jack, Queen, and King. Two suits are red in color: hearts and diamonds. Two suits are black in color: clubs and spades. Use this information to compute the probabilities asked for below and leave them in fraction form. All events are in the context that three cards are dealt from a well-shuffled deck without replacement.

a. The first and second cards are both hearts.
b. The third card is an eight.
c. None of the three cards is an ace.

Answers

Answer 1
Answer:

Answer:

a)  13/52    and the second  12/51

b) Two solutions:

b.1 if we did not picked up an eight in the first two cards   4/50

b.2 there is an eight i the two previous    3/59

c ) (48/52)*(47/51)*(46/50)

Step-by-step explanation:

Condition: Cards are taken out without replacement

a) Probability of first card is heart

There are 52 cards and 4 suits with the same probability , so you can compute this probability in two ways

we have  13 heart cards and 52 cards  then probability of one heart card is  13/52   = 0.25

or you have 4 suits, to pick up one specific suit the probability is 1/4 = 0,25

Now we have a deck of 51 card with 12 hearts, the probability of take one heart is : 12/51

b) There are 4 eight (one for each suit )   P =  4/50 if neither the first nor the second card was an eight of heart, if in a) previous we had an eight, then this probability change to 3/50

c) The probability of the first card different from an ace is 48/52 , the probability of the second one different of an ace is 47/51 and for the thirsd card is 46/50. The probability of none of the three cards is an ace is

(48/52)*(47/51)*(46/50)


Related Questions

HIGH SCHOOL

Ria is an Indian student who was admitted to a US university. Her annual tuition is $42,000. She has to pay her tuition fees in US dollars. She needs to calculate how many Indian rupees she will need to buy one dollar. The dollar to rupee exchange rate is 63.76 and rupee to dollar exchange rate is 0.015. How many Indian rupees will Ria need to buy one dollar? 50.00 rupees

56.00 rupees

63.76 rupees

76.63 rupees

Answers

1$ = 63.76 rupees (dollar to rupee exchange)
1 rupee = 0.015$ (rupee to dollar exchange)
To buy one dollar, Ria will need 63.76$
Answer: (c)

Now, Ria's annual fees is $42,000. To know how much this is in dollars, use cross multiplication as follows:
tuition fees = (42,000*63.76) / (1) =  2,677,920 rupees

Ria will need 2677920 Rupees to pay her tuition fees

Data;

  • Tuition fee = $42,000
  • $1 = 63.76 rupees
  • $1 rupees = $0.015

How Many Rupees will she need to buy a Dollar?

We need to convert the currency from dollars to rupees

From the data given in the question, $1 is equivalent to 63.7 Rupees.

This information can further be used to determine how many Rupees she needs to pay her Tuition fees.

Ria will need 2677920 Rupees to pay her tuition fees

Learn more on conversion here;

brainly.com/question/2681210

HIGH SCHOOL

2x-5y=1 put into y=mx+b

Answers

Solve the equation for y.
2x - 5y = 1
-5y = -2x + 1
y = 2/5x -1/5
This equation is in standard form :  2x-5y=1
We need to make it slope intercept form: y = mx + b

2x - 5y = 1-2x

-5y = -2x + 1
---------------
     -5

Final answer:  y = 2/5x + -1/5

MIDDLE SCHOOL

There are 138 people seated at a table in a banquet hall. Each table can seat 12 people. All the tables are full except one. How many full tables are there.

Answers

Answer:

11 full tables.

Step-by-step explanation:

There are 138 people seated at a table in a banquet hall.

Each table can seat 12 people.

At one table there are seated = 12 people

138 people seated at the tables =

                                                     = 11.5 tables.

There are 11 full tables and one has only 6 people.


There are 11 full tables, because when you divide 138 by 12 you get 11 remainder 6. So there is 11, because 12 people are at 11 tables and 6 at one!
HIGH SCHOOL

What is the median of the data? 18, 17, 11, 18, 14, 14, 15, 18, 13, 12, 20, 17

A.
15

B.
16

C.
17

D.
18

Answers

18, 17, 11, 18, 14, 14, 15, 18, 13, 12, 20, 17

Step One: Put them in numerical order.

11, 12, 13, 14, 14, 15, 17, 17, 18, 18, 18, 20

Step Two: Cross out one from each side until you are left with one or two in the center. (ones that are crossed out will be bolded for our purposes)

11, 12, 13, 14, 14, 15, 17, 17, 18, 18, 18, 20

Step Three: Since two numbers are left in the middle, the median is the number in the middle of the two.

Median = 16 (B)
HIGH SCHOOL

Solve the inequality. –2 < 4x – 10 < 6 A. –16 < x < –8

B. 4 < x < 12

C. 2 < x < 4

D. –3 < x < –1

Answers

-2 < 4x - 10 < 6
+10. +10. +10
8 < 4x < 16
÷4. ÷4. ÷4
2 < x < 4

Answer:

+10. +10. +10

8 < 4x < 16

÷4. ÷4. ÷4

2 < x < 4


Step-by-step explanation: Please leave me as brainliest answer!!


HIGH SCHOOL

Look at this prism and its net. Rectangular prism with length labeled 5 meters, width labeled 7 meters, and height labeled 12 meters. Net of the same rectangular prism with the same dimensionsn labeled.
What is the surface area of this rectangular prism?

Answers

I hope this helps you


2.5.7+2.5.12+2.7.12


70+120+168


358

MIDDLE SCHOOL

Ethan and Ava share a reward of $84 in a ratio of 4:3. How much does Ethan get?

Answers

Okay so first you would add 4 and 3 which altogether gives you 7. So that means Ethan is going to get 4/7 of the money and Ava is going to get 3/7 of the money. So to find 4/7 of the money you multiply 4/7 times 84 and you get $48. So ethan gets $48 .
MIDDLE SCHOOL

Which pair of numbers is relatively prime? A. 7 and 21
B. 4 and 15
C. 6 and 9
D. 9 and 27

Answers

Answer:

A


Step-by-step explanation:


Answer:

4 and 15

Step-by-step explanation:

i just took the quiz and i got it right :)

MIDDLE SCHOOL

Which fraction is bigger 7/8 or 13/15

Answers

Answer:

7/8

Step-by-step explanation:

Step 1: Change the denominators so that they are the same for both fractions

7/8 x 15 = 105/120

13/15 x 8 = 104/120

Step 2: Compare

104/120 < 105/120 = 13/15 < 7/8

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