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
Sergeeva-Olga [200]
3 years ago
11

Suppose that in one metropolitan area, 25% of all home- owners are insured against earthquake damage. Four home-owners are to be

selected at random; let X denote the number among the four who have earthquake insurance. a. Find the probability distribution of X. [Hint: Let S denote a homeowner who has insurance and F one who does not. Then one possible outcome is SFSS, with probability (.25)(.75)(.25)(.25) and associated X value 3. There are 15 other outcomes.]
Mathematics
1 answer:
emmasim [6.3K]3 years ago
6 0

Answer:

Step-by-step explanation:

Given that,

25% home owners are insecure of earthquake problem

If we select 4 home owners at random

let X denote the number among the four who have earthquake insurance

Let find the probability distribution of X

Let S- denotes a home owner who has insurance

Let F denotes a home owner who does not have insurance.

Then, P(S) =25% = 0.25

P(F) = 1 — P(S) = 1 —0.25

P(F) = 0.75

The possible outcomes of X is

X(0) = If no person has insurance

X(1) = If only 1 person has insurance

X(2) = If only 2 persons has insurance

X(3) = If only 3 persons has insurance

X(4) = If only 4 persons has insurance.

The cardinality of the sample space is n(C) = 2ⁿ = 2⁴ => 16

So, the sample space is given as

{FFFF, FFFS, FFSF, FFSS, FSFF, FSFS, FSSF, FSSS, SFFF, SFFS, SFSF, SFSS, SSFF, SSFS, SSSF, SSSS}

For X=0, the possible is {FFFF} i.e. no insurance, the one without insurance.

P(X) = 0.25×0.25×0.25×0.25

P(X) = 0.25⁴

P(X) = 0.00390625

For X=1, the possible outcome are

FFFS, FFSF, FSFF, SFFF

P(X=1) = 0.25³•0.75 + 0.25³•0.75 + 0.25³•0.75 + 0.25³•0.75

P(X=1) = 0.046875

For X=2 the possible outcomes are

FFSS, FSFS, FSSF, SFFS, SFSF, SSFF,

P(X=2)=0.25²•0.75²+0.25²•0.75²+ 0.25²•0.75²+ 0.25²•0.75²+ 0.25²•0.75²+ 0.25²•0.75²

P(X=2) = 0.2109375

For X=3 the possible outcomes are

FSSS, SFSS, SSFS, SSSF

P(X=3) = 0.25•0.75³+0.25•0.75³+ 0.25•0.75³+0.25•0.75³

P(X=3) = 0.421875

X=4 the possible outcomes are

SSSS

P(X=4) = 0.75×0.75×0.75×0.75

P(X=4) = 0.31640625.

Or

Using normal distribution

P(X=k) = ⁿCk • 0.25^k • 0.75^(4-k)

So,

P(X=0) = 4C0 • 0.25^0 • 0.75^4

P(X=0) = 0.31640625

P(X=1) = 4C1 • 0.25^1 • 0.75^3

P(X=1) = 0.421875

P(X=2) = 4C2 • 0.25^2 • 0.75^2

P(X=2) = 0.2109375

P(X=3) = 4C3 • 0.25^3 • 0.75^1

P(X=3) = 0.046875

P(X=4) = 4C4 • 0.25^4 • 0.75^0

P(X=4) = 0.00390625.

You might be interested in
Consider the system of differential equations dxdt=−4ydydt=−4x. Convert this system to a second order differential equation in y
koban [17]

\dfrac{\mathrm dy}{\mathrm dt}=-4x\implies x=-\dfrac14\dfrac{\mathrm dy}{\mathrm dt}\implies\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}

Substituting this into the other ODE gives

-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}=-4y\implies y''-16y=0

Since x(t)=-\dfrac14y'(t), it follows that x(0)=-\dfrac14y'(0)=4\implies y'(0)=-16. The ODE in y has characteristic equation

r^2-16=0

with roots r=\pm4, admitting the characteristic solution

y_c=C_1e^{4t}+C_2e^{-4t}

From the initial conditions we get

y(0)=5\implies 5=C_1+C_2

y'(0)=16\implies-16=4C_1-4C_2

\implies C_1=\dfrac12,C_2=\dfrac92

So we have

\boxed{y(t)=\dfrac12e^{4t}+\dfrac92e^{-4t}}

Take the derivative and multiply it by -1/4 to get the solution for x(t):

-\dfrac14y'(t)=\boxed{x(t)=-\dfrac12e^{4t}+\dfrac92e^{-4t}}

7 0
3 years ago
Describe the error in using properties of parallelograms.
Bogdan [553]

Answer:

get rekt

Step-by-step explanation:

3 0
3 years ago
2-31. Write an equation and solve it to find the answer to the question below.  Use the 5-D Process to help you write the equati
raketka [301]

r = 25+b

n = 3b

n+r+b=435

3b+25+b+b=435

5b+25=435

5b=210

b=42

r = 25+42 = 67

n = 3(42) = 126

6 0
3 years ago
A line passes through the points (7, 10) and (7, 20). Which statement is true about the line?
saul85 [17]
It has no slope 
a vertical line 
x=7


4 0
3 years ago
Read 2 more answers
I need helppppppp plzzzzzz
Zanzabum
14 x 10^3 = 14,000 (the elephants weight)

So the cat weighs 14 pounds
3 0
3 years ago
Read 2 more answers
Other questions:
  • Is 2,-5,-12,-19,-26 an arithmetic sequence
    12·2 answers
  • What is the value of 18 powered by 2? 36 ,324, 360 ,9
    13·2 answers
  • 2. Josh has m marbles. Matthew has 5 more than triple the number of marbles that Josh has. In terms of m, how many marbles does
    9·1 answer
  • how to find the area of two-dimensional and three-dimensional shapes? Please put small words so I will understand it ty :]
    9·1 answer
  • Construct a mathematical inequality or equation to express the following sentence:
    11·2 answers
  • Please help me in this question.<br> Am new to this chapter.
    14·1 answer
  • What is the slope of a line that passes through points (-1, 4) and (4, 9)?
    10·1 answer
  • A boy pushes a bike with 5 newtons up a hill that is 300 meter long. How much work does he do?
    7·1 answer
  • Solve the system<br> y=x2 +4x + 3<br> y= 4x + 12<br> Enter your answers in the boxes.
    10·1 answer
  • The weights of 5 girls are 70 pounds, 68 pounds, 85 pounds, 62 pounds, and 70 pounds. Nina finds measures of center and measures
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!