Three cards are selected one after the other from a standard deck of 52 cards.
What is the probability that all three cards are spades if none of the first two cards is replaced?

Answers

Answer 1

Answer:

[tex]\frac{11}{850}[/tex]

Step-by-step explanation:

Let's see

The probability of the first card being a spade is 13/52 (as there's 13 spades in the deck.

The probability for the second card is 12/51 (because there's 12 spades left in 51 cards total).

The probability for the third is - you guessed it! - 11/50

so the total probability is:

[tex]\frac{13}{52} \cdot \frac{12}{51} \cdot \frac{11}{50} = \frac{1}{4} \cdot \frac{4}{17} \cdot \frac{11}{50} = \frac{1}{17} \cdot \frac{11}{50} = \frac{11}{850}[/tex]

A more generic solution:

Let's use the binomials to find the solution with combinations:

We need to pick 3 cards out of 13. This can be done in

[tex]\binom{13}{3} = \frac{13!}{3!\cdot10!}[/tex] ways.

And the total number of ways to pick 3 cards out of 52 is:

[tex]\binom{52}{3} = \frac{52!}{3!\cdot 49!}[/tex]

So the probability is:

[tex]\frac{ \binom{13}{3} }{ \binom{52}{3} } = \frac{ \frac{13!}{3!\cdot 10!} }{ \frac{52!}{3!\cdot 49!} } = \frac{ \frac{13!}{10!} }{ \frac{52!}{49!} } = \frac{13 \cdot 12 \cdot 11}{52 \cdot 51 \cdot 50}[/tex]

Which again brings us to the result computed before.


Related Questions

What are the factors of the equation x 2 - 5x + 6?

Answers

Answer:

(x-3)(x-2)

Step-by-step explanation:

x^2 -5x+6

What two numbers multiply to 6 and add to -5

-3 * -2 = 6

-3 -2 = -5

(x-3)(x-2)

veterinary doctors marked 30 deer and released them. Later on they counted 150 deer, 12 of which had marks. TO the nearest whole number, find the best estimate of deer population.

Answers

Answer:

1800

Step-by-step explanation:

the temperature at 3 p.m. was 35 Fahrenheit. the temperature had dropped 45 degrees by 9 p.m. . what's the temperature in degrees Fahrenheit at 9 p.m.?​

Answers

-15 degrees Fahrenheit

3 four drinks at Starbucks cost $14.00. How much do 7 drinks cost?

Answers

Answer:

32.2

Step-by-step explanation:

divide 14 by 3 to get 4.6 then you multiply 7 by 4.6

Hope this helped you

what is the answer to (12+12)x19/2

Answers

Answer:

Use Photo Math, it will explain all the steps.

Multiply (3x-5)(x+4)

Answers

Answer:

3x^2+7x-20

Step-by-step explanation:

Answer:

expand the brackets

3x^2 + 7x -20

Step-by-step explanation:

(3x-5)(x+4)

= 3x^2 + 12x - 5x + 20

= 3x^2 + 7x + 20

Ms. Applegate rented a car for a vacation. She had to pay $15 to rent the car. Then, she paid $10 per
day while she used the car. If the final bill was $45, how many days did Ms. Applegate rent the car
for?

Answers

Answer:

she used the car for 3 days

Step-by-step explanation:

1. = 10$

2. =10$

3. =10$

the rent was 15$ so 30 + 15 =45$

Answer:

yay i got the spam answerer reported

Step-by-step explanation:

please help me with this problem i give brainiest.

Answers

Answer:

This is the answer in dollar

35x+9<=310

write an equation to math the vertical line shown

Answers

Answer:

x=1

Step-by-step explanation:

We know this, because the value of x is always constant, no matter the y-value. So, the equation is x=1.

Hope this helped!

X=1 hope that helps !!!

The circumference of a circle is approximately 131.88 centimeters What is the area of the shaded region (6/10 of a circle)

Answers

Answer:

82.97cm^2

Step-by-step explanation:

Given data

Circumference=  131.88 centimeters

We want to find the area of 6/10 part of a circle

Firstly, let us find the area of the circle

We need to get the radius

C= 2πr

131.88= 2*3.142*r

131.88=6.284r

r=  131.88/6.284

r=20.98 cm

Area= πr^2

Area= 3.142*20.98^2

Area= 3.142*440.16

Area= 1382.98cm^2

Hence 6/10 of a 1382.98

=0.06*1382.98

=82.97cm^2

Eric's Lawn Service charges a one-time fee of $10, in addition to $15 her hours worked. Which expression represents how much money they would charge if they worked n hours? *​

Answers

Answer:

15

Step-by-step explanation:

$10 is only a one time fee, that means you will never have to pay 10 dollars again, but 15 dollars is the hourly rate, so each hour goes by, your charged 15 dollars so the answer is 15 dollars

“If Teresa’s daughter is my daughter’s mother, what am I to Teresa?”
a) Grandmother

b) Mother

c) Daughter

d) Granddaughter

e) I am Teresa

Answers

Answer:

Step-by-step explanation:

grandmother

Answer:

C) Daughter

Step-by-step explanation:

Why is this so hard

val Verde Unified SD
https://my.hrw.cc
& Co my.hrw.com/wwtb/api/viewer.pl
Personal Math Trainer Lesson 6.2 - Homework - Homework
112131415161718
9
10
Gordon types 1,612 words in 26 minutes. Find the unit rate.
Gordon types
words per minute.

Answers

Answer:

nothing to do with your question just need points

Step-by-step explanation:

Answer:

62 Words Per Minute

Step-by-step explanation:

Big brain go thinky-think.

In which situation would you most likely use a credit card?

Answers

Answer:

A

Step-by-step explanation:

Answer:

The unexpected leak.

Step-by-step explanation:

use it for a good cause please.

brainliest?

Please help as soon as possibly will give brainliest

Answers

It’s the first one because there is a pattern and nor X or Y repeat

Answer:

The last option.

Step-by-step explanation:

Because, x*5 each time, gets you y.

ONLY GIVING BRAINLYEST IF YOU ANSWER QUICKLY AND CORRECTLY
A student attempted to generate an equivalent expression using the distributive property, as shown below:

7(y − 5) = y − 35

What was the mistake made?

a
7 was not multiplied by y

b
7 was not multiplied by −5

c
Incorrect sign was used for the first term

d
Incorrect sign was used for the second term

Answers

Answer:

A: 7 was not multiplyed by Y

Step-by-step explanation:

I learned it in math class last year.

Answer:

option A is correct answer

Step-by-step explanation:

=> 7 was not multiplied by y

=> hope it helps

A golf group planned a trip to Squaw Valley, and 104 of the members signed up to go. If this is 10% of the group, how many members does the golf group have in total?
Group of answer choices

a 1040 members

b 114 members

c 110 members

d 204 members

Answers

A 1040 is the answer

whoever can help me will gwt the brainliest!​

Answers

Answer:

9. 7*12*14=1176

10. 6*5*8=240

11.6*8*15=720

12. 11*5*9=495

13.  7*16*28=3136

14. 13*8*24=2496

Can someone help me i will give brainleast and no links I really need to finish this I have 15 left

Answers

1.) 5+5x=y (I think it’s y)
2.) mark (0,5) (1,10) (2,15) (3,20) (4,25) and so on
3.)yes because each minute that passes it fills 5 gallons
4.) instead of started at (0,5) it would start at (0,0)
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6.) 40+8x=t, 40 represents how much he started with, 8 represents how much a day he gets, x represents how many days, and t is the total

I=$200,p=$1000,r=4 years

Answers

Answer:

idt this is right..... sorry if this is wrong...

Step-by-step explanation:

I = $ 8,000.00

Equation:

I = Prt

Calculation:

First, converting R percent to r a decimal

r = R/100 = 200%/100 = 2 per year,

then, solving our equation

I = 1000 × 2 × 4 = 8000

I = $ 8,000.00

The simple interest accumulated

on a principal of $ 1,000.00

at a rate of 200% per year

for 4 years is $ 8,000.00.

A basket contains four apples, three
peaches, and four pears. You randomly
select a piece of fruit. It is an apple or a
peach. What the probability

Answers

I think it is a 95 % you pick a apple or a peach because you won’t know I till you look at it

Pls help fast stuck on the last question and it’s due soon:(

Answers

Approximately 14.036

please help its due tomorrow!!

Answers

If you can give me a few minutes I should have it done

Help me with this!!!!

Answers

Well the distance from the two points is 15 so that means the midpoint in -10+7.5=-2.5. There you go! Have a nice day.

CALCULATE ANGLES USING LINE AND ANGLE RELATIONSHIPS:) will mark b for right answer

Answers

Answer:

           a = 62°

Step-by-step explanation:

a = 360° - (243° + 55°) = 360° - 298° = 62°

solve -4x^2+3x=-5 using quadratic formula​

Answers

Answer:

Step-by-step explanation:

Here, we want to solve the given quadratic equation using the quadratic formula

We need to rewrite the equation in the standard form;

-4x^2 + 3x + 5 = 0

we have the value a as -4

value b as 3

C = 5

we then substitute these values into the quadratic formula as seen in the attachment

What is the measure of

Answers

Answer:

27

Step-by-step explanation:

Answer: I'm thinking 27 but not sure though.

Step-by-step explanation:

ASAP NO SENDING LINKS

Answers

Answer:

Matt made the error

He used the diameter instead of the radius in step 2

Step-by-step explanation:

19) The city of Amsterdam is 12 meters below sea level. Lammefjord, a city in Denmark, is 17
meters below sea level. How much higher is Amsterdam than Lammefjord?

Answers

Answer:

Amsterdam is 5 meters higher than Lammefjord.

Step-by-step explanation:

17 m - 12 m = 5 m

explain why 8.0 is greater then 0.8

Answers

Answer:

since the eight in the second number is to the right of the decimal, and there id no other number on the left, the second number isn't even a whole number. It is four fifths of a whole. while the eight in the first number is to the left of the decimal it is a whole number eight times. like, which is more eight cookies or a part of one cookie.

Step-by-step explanation:

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