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
taurus [48]
3 years ago
15

An e-mail filter is planned to separate valid e-mails from spam. The word free occurs in 60% of the spam messages and only 4% of

the valid messages. Also, 20% of the messages are spam.
1. Determine the following probabilities:
a. The message contains free.
b. The message is spam given that it contains free.
c. The message is valid given that it does not contain free.
Mathematics
1 answer:
ANEK [815]3 years ago
4 0

Answer:

(a) 0.152

(b) 0.789

(c) 0.906

Step-by-step explanation:

Let's denote the events as follows:

<em>F</em> = The word free occurs in an email

<em>S</em> = The email is spam

<em>V</em> = The email is valid.

The information provided to us are:

  • The probability of the word free occurring in a spam message is,             P(F|S)=0.60
  • The probability of the word free occurring in a valid message is,             P(F|V)=0.04
  • The probability of spam messages is,

        P(S)=0.20

First let's compute the probability of valid messages:

P (V) = 1 - P(S)\\=1-0.20\\=0.80

(a)

To compute the probability of messages that contains the word free use the rule of total probability.

The rule of total probability is:

P(A)=P(A|B)P(B)+P(A|B^{c})P(B^{c})

The probability that a message contains the word free is:

P(F)=P(F|S)P(S)+P(F|V)P(V)\\=(0.60*0.20)+(0.04*0.80)\\=0.152\\

The probability of a message containing the word free is 0.152

(b)

To compute the probability of messages that are spam given that they contain the word free use the Bayes' Theorem.

The Bayes' theorem is used to determine the probability of an event based on the fact that another event has already occurred. That is,

P(A|B)=\frac{P(B|A)P(A)}{P(B)}

The probability that a message is spam provided that it contains free is:

P(S|F)=\frac{P(F|S)P(S)}{P(F)}\\=\frac{0.60*0.20}{0.152} \\=0.78947\\

The probability that a message is spam provided that it contains free is approximately 0.789.

(c)

To compute the probability of messages that are valid given that they do not contain the word free use the Bayes' Theorem. That is,

P(A|B)=\frac{P(B|A)P(A)}{P(B)}

The probability that a message is valid provided that it does not contain free is:

P(V|F^{c})=\frac{P(F^{c}|V)P(V)}{P(F^{c})} \\=\frac{(1-P(F|V))P(V)}{1-P(F)}\\=\frac{(1-0.04)*0.80}{1-0.152} \\=0.90566

The probability that a message is valid provided that it does not contain free is approximately 0.906.

You might be interested in
How to graph circles​
Lyrx [107]

Answer:

{x}^{2}  +  {y}^{2}  =  {r}^{2}

5 0
3 years ago
Charles bought a box of fruit that contained only oranges and tangerines.
cupoosta [38]

Answer:xxx

  1. c i got c is the awnser

Step-by-step explanation:

6 0
3 years ago
a triangle has side lengths of (2.9n-7.8p)(2.9n−7.8p) centimeters, (6.6n-6.4q)(6.6n−6.4q) centimeters, and (2.9q-3.8p)(2.9q−3.8p
krok68 [10]

The perimeter of the triangle is: (9.5n - 11.6p - 3.5q) cm.

<h3>What is the Perimeter of a Triangle?</h3>

The total length of all the sides of a triangle is equal to the perimeter of the triangle.

Given a triangle has the following lengths:

  • (2.9n-7.8p) centimeters,
  • (6.6n-6.4q) centimeters,
  • (2.9q-3.8p) centimeters.

The perimeter of the triangle = (2.9n-7.8p) + (6.6n-6.4q) + (2.9q-3.8p)

The perimeter of the triangle = 2.9n - 7.8p + 6.6n - 6.4q + 2.9q - 3.8p

Combine like terms together

The perimeter of the triangle = 2.9n + 6.6n - 7.8p - 3.8p - 6.4q + 2.9q

The perimeter of the triangle = 9.5n - 11.6p - 3.5q

Thus, the perimeter of the triangle is: (9.5n - 11.6p - 3.5q) cm.

Learn more about the perimeter of the triangle on:

brainly.com/question/24382052

#SPJ1

4 0
2 years ago
Find the polar equation for the cartesian curve x^2-y^2 = sqrt(x^2+y^2)
cestrela7 [59]

ANSWER:

r = \frac{1}{cos2(theta)}

Explaination:

Convert the given curve into the the polar form.

x = rcosθ

y = rsinθ

in f(x,y) = (x²-y²) - √(x²+y²) = 0

put the values of x & y in given curve equation.

We get at,

g(r,θ) = (r²cos²θ - r²sin²θ) - √(r²cos²θ + r²sin²θ) = 0

g(r,θ) = r²(cos²θ - sin²θ) - √r² = 0

We know that,

cos²θ - sin²θ = cos2θ

g(r,θ) = r²(cos2θ) - r = 0

Solve for r

Finally we get:

r = \frac{1}{cos2(theta)}

8 0
3 years ago
The value of x for which the expressions 5(3x-4) equal to 2(2x+1)
notsponge [240]

Answer:

the value of x is 2.

Step-by-step explanation:

5(3x - 4) = 2(2x + 1)

15x - 20 = 4x + 2

15x - 4x = 2 + 20

11x = 22

x = 22/11

x = 2

5 0
3 years ago
Other questions:
  • Shelly hopped onto her bicycle and pedaled to the park at 14 miles per hour. Then she whizzed back at 20 miles per hour. If the
    14·1 answer
  • How to solve percent of change
    14·1 answer
  • If five books cost 5.25 how much would 3 cost.
    8·1 answer
  • Name Five countries through which the Equator passes
    11·2 answers
  • What am i supposed to do here im so confused.
    10·2 answers
  • What is -6.1 as a fraction​
    11·1 answer
  • As altitude within the troposphere increases, the amount of water vapor in the atmosphere generally: PLEASE HELP ME!!!
    11·1 answer
  • Please help I'm tired asking 11 times
    9·1 answer
  • Can you please help me with this last question? I'm stuck​
    9·1 answer
  • Please help me answer these.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!