Mathematics College

An experiment consists of ranomly drawing three cards in succession without replacement from a standard deck of 52 cards. Let A be the event of a king on the first draw, B the event of a king on the second draw, and C the even of a king on the third draw. Describe each of the events listed below and calculate its probability.

a. A ∩ B
b. A U B
c. A ∩ B ∩ C
d. A U B U C

Answers

Answer 1

Answer:

0.0045248 ;

0.1312218 ;

0.0001809 ;

0.1659729

Step-by-step explanation:

Number of Kings in deck = 4

Total number of cards in deck = 52

Picking without replacement :

A = King on first draw :

P(A) = 4 / 52

A = King on 2nd draw :

P(B) = 3 / 51

A = King on 3rd draw :

P(C) = 2 / 50

1.) P(A n B) = P(A) * P(B)

P(A n B) = 4/52 * 3/51 = 12 / 2652 = 0.0045248

2.) P(A u B) = P(A) + P(B) - P(AnB)

P(AuB) = 4/52 + 3/51 - 0.0045248 = 0.1312218

3.) P(A ∩ B ∩ C) = P(A) * P(B) * P(C)

P(A ∩ B ∩ C) = 4/52 * 3/51 * 2/50 = 0.0001809

4.) P(A U B U C) =

P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) - P(AnBnC)

P(AnC) = P(A) * P(C) = 4/52 * 2/50 = 0.0030769

P(BnC) = P(B) * P(C) = 3/51 * 2/50 = 0.0023529

4/52 + 3/51 + 2/50 - 0.0045248 - 0.0030769 - 0.0023529 + 0.0001809 = 0.1659729

Related Questions

Given that x is an integer and that –15 <x 5 35,
write down the least value of x.

Answers

Answer:

a) d = 3 b) a(n) = 3n – 13 c) a(27) = 68

Step-by-step explanation:

solutions are (x, y) = (29,13) and (9349, 4181), which lead to (a, b) = (15,5) and (4895 ... corresponding to integer values of x give the quadruples. (x, y, z ... Since no number congruent to 3, modulo 4, can be written as the sum of two squares ... k is odd, the equation x2 - (k2 - 4)y2 = 4 has smallest solution in positive integers .

Which is a possible solution for -4 LaTeX: >> X

Answers

[tex] \text { > }[/tex]

\tex {>} is to be written

5m - 4z + 8m + 3 – 2z

Answers

Answer:

Step-by-step explanation:

5m+8m= 13m

-4z-2z= -6z

= 13m-6z+3

Answer:

13m - 6z + 3

Step-by-step explanation:

Kecia made a password that consists of 4 digits, 0-9. None of the digits are the same. How many possible passwords did Kecia choose from? (HOW DID YOU GET YOUR ANSWER PLEASE SHOW YOUR WORK!!)

A. 70%
B. 5040
C. 5.2
D. 4(2X+4)
E. 300%
F. 2.5
G. 5267
H. 4X(2X-4)
I. 299%
J. .4

Answers

Answer:

There are 9 possible numbers for the first number. There are 8 possible numbers for the second number since one number has been picked. For the third number there are 7 possible numbers.

9*8*7=5040

Step-by-step explanation:

Evaluate −6 − (−4). (10 point)
−10
−2
24
2

Answers

Answer: negative 2 (-2)

Step-by-step explanation:-6+4=-2

Answer:

−2

Step-by-step explanation:

−6 − (−4)

= −6 − (−4)

= −6 + 4

= −2

Sasha spins the spinner shown below.
H
IF Sasha spins the spinner once, what is the
probability it will land on or G?
w

Answers

Answer:1/7

Step-by-step explanation:

Chad's bedroom floor is 18 feet long and 13 feet wide. He has an area rug on his floor that is 2 feet long and 8 feet wide.

Which statement tells how to find the amount of the floor that is not covered by the rug? Select all that apply.

A Add 18 × 13 and 2 × 8.
B Add 18 + 13 + 2 + 8.
C Subtract 18 × 13 from 2 × 8.
D Subtract 2 × 8 from 18 × 13.
E Subtract 16 from 18 × 13.
F Subtract 13 × 8 from 18 × 2.

Answers

9514 1404 393

Answer:

D Subtract 2 × 8 from 18 × 13.E Subtract 16 from 18 × 13.

Step-by-step explanation:

To find the area not covered, the rug area must be subtracted from the floor area. Each of those areas is the product of their respective dimensions. The statements describing that subtraction are ...

D Subtract 2 × 8 from 18 × 13.

E Subtract 16 from 18 × 13.

If X = 14, find the value of the variable a. If your answer is not an integer, express it in simplest radical form.

Answers

Answer:

Step-by-step explanation:

First thing I would do is square the 14, and put it under the radical. Itll make the calculations a little bit easier.

14sqrt(2) = sqrt392

Use the definition of sine to find the value of a

sin(45) = opposite/hypotenuse = a/sqrt392

[tex]sin(45)=\frac{a}{\sqrt{392} }[/tex]

a = 14

A class is collecting data on the number of pets each student has. The class is divided into 4 groups. Which table shows the group of students with the greatest mean number of pets?

Answers

Answer:

The group of students on the top right those students have a mean of 2.6

Step-by-step explanation:

The mean is adding up all the different numbers of pets for each kid and dividing it by the number of kids so 13 the number of pets and 5 the number of different students

Help me please guys.
Find the measure of angle b using the law of sines.
I need to show full work to the teacher

Answers

15.04 degrees or answer A is correct.

The Law of Sines is the relationship between the sides and angles of non-right (oblique) triangles . Simply, it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle. The formula for it is A=b•sin a/sin b.

You can transform the law of sines formulas to solve some problems of triangulation (solving a triangle). You can use them to find:

The remaining sides of a triangle, knowing two angles and one side.
The third side of a triangle, knowing two sides and one of the non-enclosed angles. In some cases (ambiguous cases) there may be two solutions to the same triangle. If the following conditions are fulfilled, your triangle may be an ambiguous case:
You only know the angle α and sides a and c;
Angle α is acute (α < 90°);
a is shorter than c (a < c);
a is longer than the altitude h from angle β, where h = c * sin(α) (a > c * sin(α)).

I hate useless complicated math lol ;)

If you are the sole owner of a company with a net worth of $2.35 million dollars and are sued for $4 million dollars what is the amount that you must pay in the lawsuit? Why do you have to pay the amount that you stated?

Answers

Explanation: Well in my opinion.... Your networth doesn't matter its just showing how much money you spent...

Soo if you had $4 Million you'd pay it automatically.

Elliott took a survey for Turkey Filet. 18 students prefer turkey tenders and 12 students prefer fried turkey sandwiches with pickles on buttered buns. What percentage of students prefer turkey tenders?

Answers

Answer: 60%

Step-by-step explanation: multiply 18 by 100 than divide by 30

x-10= 30 Which value of x makes the equation true

Answers

I’m sure x equals 40

Maria earned a score of 80% on her math test. Each question on the quiz was worth 1 point, and Maria got 12 questions correct. How many questions were on the quiz?

Answers

Answer:

15 questions were on the quiz

Step-by-step explanation:

12/15 = .80 = 80%

Answer:

68?

Step-by-step explanation:

Pls help periodddd pooh

Answers

Answer:

the answer is n = -7

I also put a image to show you how to solve the equation. I hope the image helps.

Answer:

n= -7

Step-by-step explanation:

pls help me:(!!!!!!!!!!

Answers

Answer:

A.........................

Hello, how are you?. I need help. Do you know where they sell teething toys for puppies in California?

Answers

Petco has a bunch of stuff for puppies

I need help with this to I just want to make sure I’m right or wrong.!

Answers

i’m pretty sure you’re right. hope this helps:)

Answer:

the answer is D

Step-by-step explanation:

Ivan started the week on page 35 of his book and read 20 pages each night. What page will Ivan be on if he reads for 8 nights?

Answers

Answer: he should be on page 195

Step-by-step explanation:

Ben is thinking of two numbers. Their sum is -10 and their difference is -2.

Answers

Answer:

ben is thinking of the equation -10 minus -8 and the answer for the problem is -2

Step-by-step explanation:

Drag each equation to show if it could be a correct first step to solving the equation 3(6+x)=24.

ANSWER FAST PLEASE

Answers

Answer:

x=2

Step-by-step explanation:

It's 18+ 3x = 24 and (3.6) + (3.x) = 24

4x + 6°
6x - 100
7x + 14°

Answers

9514 1404 393

Answer:

x = 10°; angles are 50°, 46°, 84° (CW from left)

Step-by-step explanation:

The sum of the three angles is 180°, so ...

(6x +10°) +(4x +6°) +(7x +14°) = 180°

17x +10° = 180°

17x = 170°

x = 10°

Then the angles are ...

6x -10° = 6·10° -10° = 50°

4x +6° - 4·10° +6° = 46°

7x +14° = 7·10° +14° = 84°

What is the solution to the system of linear equations graphed here?
A (2, -1)
B) (-1,2)
C (2, 1)
D) No Solution

Answers

Answer:

the solution is (-1, 2).

PLS HELP ME AGAIN SMART PEOPLE I NEED A GOOD ANSWER PLSS IM CRYING

Answers

Answer:

1.b

2.d

Step-by-step explanation:

1.6(3x + 5) = 18x + 30 = 15x + 30 + 3x.

SO, the ? is equal to 30.

2. d

Find the gradient of the line segment between the points (2,-3) and (-3,-8)

Answers

Answer:

Step-by-step explanation:

gradient=

[tex] \frac{ - 8 - ( - 3)}{ - 3 - 2} = \frac{ - 8 + 3}{ - 5} = \frac{ - 5}{ - 5} = 1[/tex]

hello i am not that good at math and i struggle with fractions

problem: “divide 2/8 by 9/18. Input your answer as a reduced fraction”

how do i do that?? how do i divide fractions and reduce them?

Answers

Answer:

the answer is 1/2 or 0.5

Step-by-step explanation:

So basically you just get on a calculator and divide it after you do that it will give you a decimal and all you have to do is convert that decimal to a fractiom so we know that 0.5 is a half so therefore 0.5=1/4

Three fourths of the product of four fifths and fifteen

Answers

Answer:

I think it is 9

Step-by-step explanation:

Answer:

The answer is 9

Step-by-step explanation:

15 * [tex]\frac{4}{5}[/tex] * [tex]\frac{3}{4}[/tex] = 15 * [tex]\frac{3}{5}[/tex] = 9

F(x) = 2x^3 + 5x^2 -6x-7 g(x) = 2x-3 find (f - g) (x)

Answers

Given:

The function are:

[tex]f(x)=2x^3+5x^2-6x-7[/tex]

[tex]g(x)=2x-3[/tex]

To find:

The function (f-g)(x).

Solution:

We have,

[tex]f(x)=2x^3+5x^2-6x-7[/tex]

[tex]g(x)=2x-3[/tex]

We need find (f-g)(x).

[tex](f-g)(x)=f(x)-g(x)[/tex]

[tex](f-g)(x)=2x^3+5x^2-6x-7-(2x-3)[/tex]

[tex](f-g)(x)=2x^3+5x^2-6x-7-2x+3[/tex]

On combining like terms, we get

[tex](f-g)(x)=2x^3+5x^2+(-6x-2x)+(-7+3)[/tex]

[tex](f-g)(x)=2x^3+5x^2-8x-4[/tex]

Therefore, the correct option is B.

9x^{2} - x^{3} - 9 + x
What is ^^^ factored?

Answers

Step-by-step explanation:

9x² - x³ - 9 + x

factored = x²(9 - x) - (9 - x)

= (9 - x)(x² - 1)

= (9 - x)(x + 1)(x - 1)

5) 9x + 8y = -2
-5x + 8y = 26
A) (2, 2)
C) (2,-2)
B) (-2,-2)
D) (-2, 2)

Answers

Answer:

5)9x+8y=-2

-5x+8y=26

A) (2,2)

the anwser is A :))))

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