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
gavmur [86]
3 years ago
10

In a certain town in the united states, 40% of the population are democrats and 60% are republicans. The municipal government ha

s proposed making gun ownership illegal in the town. It is known that 75% of democrats and 30% of republicans support this measure. If a resident of the town is selected at random.
(a) what is the probability that they support the measure?
(b) if the selected person does support the measure what is the probability the person is a democrat?
(c) if the person selected does not support the measure, what is the probability that he or she is a democrat?
Mathematics
1 answer:
mixer [17]3 years ago
4 0

Answer:

(a) 0.48, (b) 0.625, (c) 0.1923

Step-by-step explanation:

First define

Probability a person is a democrat: P(D) = 0.4

Probability a person is a republican: P(R) = 0.6

Probability a person support the measure given that the person is a democrat: P(SM | D) = 0.75

Probability a person support the measure given that the person is a republican: P(SM | R) = 0.3

Now for the Theorem of total probabilities we have

(a) P(SM) = P(SM | D)P(D)+P(SM | R)P(R) = (0.75)(0.4)+(0.3)(0.6) = 0.48

and for the Bayes' Formula we have

(b) P(D | SM) = P(SM | D)P(D)/[P(SM | D)P(D)+P(SM | R)P(R)] = (0.75)(0.4)/0.48 = 0.625

Now let SMc be the complement of support the measure, i.e.,

P(SMc | D) = 0.25 : Probability a person does not support the measure given that the person is a democrat

P(SMc | R) = 0.7: Probability a person does not support the measure given that the person is a republican,

and also for the Bayes' Formula we have

(c) P(D | SMc) = P(SMc | D)P(D)/[P(SMc | D)P(D)+P(SMc | R)P(R)] = (0.25)(0.4)/[(0.25)(0.4)+(0.7)(0.6)] = 0.1/(0.52)=0.1923

You might be interested in
Use the point-slope form linear equation given.
Agata [3.3K]

y-3=3(x+1)

opening the bracket

y-3=3x+3

y=3x+3+3

equation of the line in the form y=mx+c;

y=3x+6

therefore gradient=3

parallel lines have same gradient therefore gradient of the other line is 3

y--3/x-0=3

y+3=3(x-0)

y+3=3x-0

y=3x-3.

8 0
2 years ago
Find the area of the shaded portion in the equilateral triangle with sides 6.
LUCKY_DIMON [66]
Triangle is equilateral with sides of 6.
Therefore all angles = 60°
Ht of 30-60-90 is 3sr3 = 5.196
Area of 30-60-90 = 1/2×b×h = 3×5.196
Area = 15.59
Pie slice from each corner = 60/360×pi×r^2, with r = 3
1/6×pi×9 = 4.71 × 3 pie slices = 14.13
So, shaded inner region = area triangle - 3 pie corners = 15.59-14.13
= 1.46
7 0
2 years ago
Which graph shows a line that is perpendicular to line AB?
kherson [118]
The 3rd slot is the answer you are looking for
5 0
3 years ago
The supplement of an angle is three times the measure of the angle.
stira [4]

Answer: The angle equals  45 ∘  and the supplement is  135 ∘

Explanation:

Since the supplement is three times the angle, we can say    s  =  3 a

Since we know the supplement is  

180 − a , we can plug that in.

180 - a = 3a

180  = 4 a  (add  a  to both sides)

45  =  a  (divide both sides by  4)

Since we know the angle now, all we have to do is multiply it times  3  to find the supplement.

45  ×  3  =  135

4 0
2 years ago
A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Four hu
castortr0y [4]

<em>Answer: h = 120 ft;    w = 80 ft </em>

<em></em>

<em>A = 9600 ft^2</em>

<em />

<em>Step-by-step explanation: Let h and w be the dimensions of the playground. The area is given by:</em>

<em></em>

<em>A = h*w   (eq1)</em>

<em></em>

<em>The total amount of fence used is:</em>

<em></em>

<em>L = 2*h + 2*w + w    (eq2)    (an extra distance w beacuse of the division)</em>

<em></em>

<em>Solving for w:</em>

<em></em>

<em>w = L - 2/3*h = 480 - 2/3*h   (eq3)  Replacing this into the area eq:</em>

<em></em>

<em></em>

<em></em>

<em>We derive this and equal zero to find its maximum:</em>

<em></em>

<em>   Solving for h:</em>

<em></em>

<em>h = 120 ft.  Replacing this into eq3:</em>

<em></em>

<em>w = 80ft</em>

<em></em>

<em>Therefore the maximum area is:</em>

<em></em>

<em>A = 9600 ft^2</em>

<em />

5 0
3 years ago
Other questions:
  • What does 2/3 * 14/6 equal. Please show work
    12·1 answer
  • Travis has 9 1/3 lb of dried beans he will pour an equal amount of beans into 5 sacks how many pounds of beans will be in each s
    6·1 answer
  • Please help solve this
    7·1 answer
  • What is the value of +(-3) 0) (-3)​
    6·1 answer
  • What would the answer be?
    13·1 answer
  • 1. Choose one kind of triangle to use for a tessellation: equilateral, isosceles, or scalene. 2. Use technology or paper to crea
    6·1 answer
  • WILL GIVE BRAINLIEST AND 15 POINTS IF YOU ANSWER MY LATEST MATH QUESTION
    11·1 answer
  • Identify the figure
    11·1 answer
  • Figure VWYX is a kite.<br> 3<br> (18x-2)<br> V<br> Y<br> (12x+2)<br> х
    10·1 answer
  • F(x) = -2x + 4<br> g(x) = 2x^2 – 2x - 8<br> Find: (gof)(x)
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!