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
zzz [600]
3 years ago
6

Consider two independent tosses of a fair coin. Let A be the event that the first toss results in heads, let B be the event that

the second toss results in heads, and let C be the event that in both tosses the coin lands on the same side. Show that the events A, B, and C are pairwise independent—that is, A and B are independent, A and C are independent, and B and C are independent—but not independent.
Mathematics
1 answer:
aliina [53]3 years ago
6 0

Answer with Step-by-step explanation:

We are given that two independent tosses of a fair coin.

Sample space={HH,HT,TH,TT}

We have to find that A, B and C are pairwise independent.

According to question

A={HH,HT}

B={HH,TH}

C={TT,HH}

A\cap B={HH}

B\cap C={HH}

A\cap C={HH}

P(E)=\frac{number\;of\;favorable\;cases}{total\;number\;of\;cases}

Using the formula

Then, we get

Total number of cases=4

Number of favorable cases to event A=2

P(A)=\frac{2}{4}=\frac{1}{2}

Number of favorable cases to event B=2

Number of favorable cases to event C=2

P(B)=\frac{2}{4}=\frac{1}{2}

P(C)=\frac{2}{4}=\frac{1}{2}

If the two events A and B are independent then

P(A)\cdot P(B)=P(A\cap B)

P(A\cap)=\frac{1}{4}

P(B\cap C)=\frac{1}{4}

P(A\cap C)=\frac{1}{4}

P(A)\cdot P(B)=\frac{1}{2}\cdot \frac{1}{2}=\frac{1}{4}

P(B)\cdot P(C)=\frac{1}{4}

P(A)\cdot P(C)=\frac{1}{4}

P(A)\cdot P(B)=P(A\cap B)

Therefore, A and B are independent

P(B)\cdot P(C)=P(B\cap C)

Therefore, B and C are independent

P(A\cap C)=P(A)\cdot P(C)

Therefore, A and C are independent.

Hence, A, B and C are pairwise independent.

You might be interested in
Find the volume of the prism. round to the nearest tenth
babymother [125]

Answer:

V = 310.5 cm³

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

<u>Geometry</u>

Volume of a Prism Formula: V = lwh

  • <em>l</em> is length
  • <em>w</em> is width
  • <em>h</em> is height

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify variables</em>

<em>l</em> = 13.8 cm

<em>w</em> = 4.5 cm

<em>h</em> = 5 cm

<u>Step 2: Solve for </u><em><u>V</u></em>

  1. Substitute in variables [Volume of a Prism Formula]:                                    V = (13.8 cm)(4.5 cm)(5 cm)
  2. Multiply:                                                                                                             V = (62.1 cm²)(5 cm)
  3. Multiply:                                                                                                             V = 310.5 cm³
6 0
2 years ago
Can someone help me with this please
stellarik [79]

Ok so we'll  go ahead and solve for y first -  we just need to get it alone on one side of the equal sign

Step 1: subtract 2x from each side

2x - 7y - 2x = 19 - 2x

This cancels out the 2x on the left, giving us

-7y = 19 - 2x

Step 2: divide both sides by -7

\frac{-7y}{-7} = \frac{19}{-7} + \frac{-2x}{-7}

This gives us

y = -19/7 + 2x/7

That should be your answer for the first question. Now solving the next parts are easy. All you need to do is plug in x.

When x = -3

y = -19/7 + 2x/7

y = -19/7 + 2(-3)/7

y = -19/7 - 6/7

y = -25/7


When x = 0

y = -19/7 + 2x/7

y = -19/7 + 2(0)/7

y = -19/7


When x = 3

y = -19/7 + 2x/7

y = -19/7 + 2(3)/7

y = -19/7 + 6/7

y = -13/7


Hope that helps! Feel free to ask if I can help with anything else :)

7 0
2 years ago
The equation h=kp describes h, the height of a stack of p pennies. A stack of 15 pennies is 24 millimeters tall. What is the val
slamgirl [31]
You plug in the values so it would be 24=15k. Divide by 15 on both sides so k=24/15=1.6. :)
8 0
3 years ago
Given the line -2 + 2y = 5 , find the perpendicular line that goes through (1, -3). HeLP ME PLEASEE QUICK
brilliants [131]

Answer:

x=1

Step-by-step explanation:

Find the negative reciprocal of the slope of the original line and use the point-slope formula  y − y 1 = m ( x − x 1 )  to find the line perpendicular to  − 2 + 2 y = 5 .

4 0
3 years ago
Bsolute Value is the distance from
Yanka [14]

Answer:

The negative integers go to the left: , , , and so on. The distance between a number's place on the number line and is called the number's absolute value The absolute value of a number is its distance from 0 on a number line..

Step-by-step explanation:

Negative

I hope this helps :)

6 0
3 years ago
Other questions:
  • If f(x) = -3x + 6 and f(x)=18<br> then what is the value of x?
    15·1 answer
  • The _________ of a fraction is the part that tells how many units the fraction contains
    12·1 answer
  • A plumber is fitting pipes for a remodeled kitchen sink. The sink requires 3 different sections of pipe; the first i feet long,
    5·1 answer
  • WHY CAN'T ANYONE HELP ME PLEASE? THANKS! A student at a university makes money by buying and selling used cars. Charles bought a
    12·1 answer
  • Find the missing angle measures:
    14·1 answer
  • Integrate 1/((x^5)*sqrt(9*x^2-1)) ...?
    8·1 answer
  • Can someone please help me on the last two . I would appreciate it so much
    14·1 answer
  • Please tell me which ones I should select!!!
    14·1 answer
  • 3. A cell phone plan costs $0.20 cents per minute. Lisa
    7·2 answers
  • Pleasee help meee it’s due at 6:00
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!