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
kupik [55]
3 years ago
12

A student S is suspected of cheating on exam, due to evidence E of cheating being present. Suppose that in the case of a cheatin

g student, evidence E is present with 60% percent probability, and in the case of a student that does not cheat, evidence E is present with a 0.01 percent probability. Suppose also that the proportion of students that cheat is 1 percent. Show all the steps including identification of what formulas/properties you used. Points will be deducted from answers if only the final answer is provided.
Required:
a. Determine the events, given probabilities and inferred probabilities.
b. Determine the probability that the evidence is present.
c. Determine the probability that S cheated given the evidence is present.
Mathematics
1 answer:
Kay [80]3 years ago
5 0

Answer:

Step-by-step explanation:

Suppose we think of an alphabet X to be the Event of the evidence.

Also, if Y be the Event of cheating; &

Y' be the Event of not involved in cheating

From the given information:

P(\dfrac{X}{Y}) = 60\% = 0.6

P(\dfrac{X}{Y'}) = 0.01\% = 0.0001

P(Y) = 0.01

Thus, P(Y') \ will\ be = 1 - P(Y)

P(Y') = 1 - 0.01

P(Y') = 0.99

The probability of cheating & the evidence is present is = P(YX)

P(YX) = P(\dfrac{X}{Y}) \ P(Y)

P(YX) =0.6 \times 0.01

P(YX) =0.006

The probabilities of not involved in cheating & the evidence are present is:

P(Y'X) = P(Y')  \times P(\dfrac{X}{Y'})

P(Y'X) = 0.99  \times 0.0001 \\ \\  P(Y'X) = 0.000099

(b)

The required probability that the evidence is present is:

P(YX  or Y'X) = 0.006 + 0.000099

P(YX  or Y'X) = 0.006099

(c)

The required probability that (S) cheat provided the evidence being present is:

Using Bayes Theorem

P(\dfrac{Y}{X}) = \dfrac{P(YX)}{P(Y)}

P(\dfrac{Y}{X}) = \dfrac{P(0.006)}{P(0.006099)}

P(\dfrac{Y}{X}) = 0.9838

You might be interested in
Functions and Transformations
DaniilM [7]

The new translated function will be more towards the origin , as the value of length is decreased , Option C is the right answer.

<h3>What is a Function ?</h3>

A function is a mathematical statement used to relate a dependent and an independent variable.

It is given that

Area of a Rectangle is 10 sq. unit

Width of the Rectangle is x unit

Length is given by  

l(x) = 10 / x

When the length of the Rectangle is increased by 1 ,

The new function will be

l(x) = 10 /(x+1)

The new translated function will be more towards the origin , as the value of length is decreased ,

This is represented by Graph 3 ,

This can be proved by keeping the value of x

let x = 2

y = 10 /3 = 3.333

This is only in the graph 3 , Therefore Option C is the right answer.

To know more about Function

brainly.com/question/12431044

#SPJ1

6 0
1 year ago
Find dy /dx of x² - 2x + 5 - 6x
BaLLatris [955]

Answer:

Step-by-step explanation:

If y=x^2-2x+5-6x then

y=x^2-8x+5 by combining like terms. (I'm thinking you might have mistyped the problem because this representation is weird).

\frac{dy}{dx}=2x-8

6 0
3 years ago
A coin weighs 4/15 ounces. A different coin weighs 1/15 ounces. How much do the two coins weigh together? Write your answer as a
olchik [2.2K]

Answer:

1/3

Step-by-step explanation:

4/15 + 1/15 = 5/15

simplified its 1/3

7 0
2 years ago
The sum of two numbers is 18 and the difference is 8
Andrews [41]

Answer:

x = 13 and y = 5

Step-by-step explanation:

x + y = 18

x - y = 8

<u>Step 1:  Find y</u>

x = 18 - y

(18 - y) - y = 8

18 - y - y - 18 = 8 - 18

-2y / -2 = -10 / -2

<em>y = 5</em>

<em />

<u>Step 2:  Plug into x + y = 18 to get x</u>

x + 5 - 5 = 18 - 5

<em>x = 13</em>

<em />

Answer:  x = 13 and y = 5

3 0
3 years ago
Question 4 of 14
uranmaximum [27]
It’s D
11x= 6x + 5x
10^2 + 6x + 5x + 3
2x(5x+3)+5x+3
8 0
3 years ago
Other questions:
  • Simplify 24x5 y6 . A) 2x2 y3 6x B) 4x2 y3 6x C) 6x2 y3 4x D) 6x2 y3 2x
    14·1 answer
  • What is the inequality
    7·1 answer
  • The value in 3 in 300 is 30 times the value of 3 in?
    14·2 answers
  • Write an equation to convert a diamond's weight in carats to its weight in milligrams. Be sure to define your variables.
    12·1 answer
  • Graph one complete cycle. Label the axes accurately.<br> y = sin πx
    5·1 answer
  • Use this numbers and make it into an expression.
    9·1 answer
  • . Bryon competes on the school debate team. He won 0.40 of the debates in which he participated. Which statement is not true abo
    5·1 answer
  • What is the domain of fff?
    8·2 answers
  • Find p(-3) if p(x)= 4x^3 - 5x^2 + 7x - 10.
    8·1 answer
  • 5 is added to a number the result multiplied by 48 give product 32, what is the original number
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!