A diagnostic test for a disease is such that it (correctly) detects the disease in 90% of the individuals who actually have the disease. Also, if a person does not have the disease, the test will report that he or she does not have it with probability 0.9. Only 1% of the population has the disease in question. If a person is chosen at random from the population and the diagnostic test indicates that she has the disease, what is the conditional probability that she does, in fact, have the disease

Answer:

8.33% probability that she does, in fact, have the disease

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Positive test

Event B: Has the disease

Probability of a positive test:

10% of 100-1 = 99%

90% of 1%

So

[tex]P(A) = 0.1*0.99 + 0.9*0.01 = 0.108[/tex]

Positive test and having the disease:

90% of 1%

[tex]P(A \cap B) = 0.9*0.01 = 0.009[/tex]

What is the conditional probability that she does, in fact, have the disease

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.009}{0.108} = 0.0833[/tex]

8.33% probability that she does, in fact, have the disease

What is the slope of the line perpendicular to
y=3x-12

Data represented by quantities is called data.

Can someone answer this please!!! I only have 5 mins and u will get Brainly too :)

What if the bag did not tell us how many total servings and only told us how many total cups?
If the bag of dry fruit has 5 cups and each serving is ¼ of a cup, how many servings would the bag have?

Are the ratios 9:15 and 3:5 equivalent

Donna and Darcy collected newspapers for recycling. Donna collected 5 3/4 pounds of newspaper. Darcy collected 2 1/4 pounds of newspaper. How much newspaper did they collect between them?

pls pls pls pls helpppp

Q1: A number minus 4 is greater than 2 times a number

potrzebuję na teraz pls

Who know this answer

what is the value of 4/15 divide 2/3

(-4)-(-2)-{(-5)-[(-7)+(-3)-(-8)]}

What fraction of the shape is shaded?

A jar contains 666 red jelly beans, 666 green jelly beans, and 666 blue jelly beans.
If we choose a jelly bean, then another jelly bean without putting the first one back in the jar, what is the probability that the first jelly bean will be green and the second will be green as well?

Please help ASAP!!!!

HELP HELP HELPPPP SOMEONE PLEASE-

A cyclist starts from the point si = (7, 7, 4) at t = 0 and moves with a constant velocity of v → =(4, 5, 5) and cyclist motion can be depicted by the expression, s = si + vt which gives position vector of cyclist. Determine the distance travelled by the cyclist between t = 4 s and t = 23 s. (Distance is in meters)
A. 154.36 m
B. 157.36 m
C. 152.36 m
D. 155.36 m

A school earns $70 from selling 50 tickets for the school play. Each ticket costs the same price.
How much does the school earn for one ticket ??

6, 2, 7, 8, 8, 8, 5, 10, 10

What is the standard deviation of the data?

2.38 first cousins
2.52 first cousins
5.65 first cousins
6.36 first cousins

Pls answer this for mw​

Shawna went shopping at the thrift store yesterday and came home with 12 items and she only spent $31.50. She only got shirts and pants. If each shirt cost $2 and each pair of pants cost $3.50, which system of equations would represent this situation?

Write the pair of fractions as a pair of fractions with
common denominator
1/2 and 1/3

Angie has 3 pink bows, 1 blue bow, and 6 purple bows in a box. She will randomly choose 1 bow from the box.
What is the probability Angie will choose a purple bow?

Page 153
30. A car's value is a function of many things,
including the total mileage on the car. The
following graph illustrates the depreciation of a
car as more miles are driven. Find the value of
f(50,000) and explain its meaning. What is the
range of this function?
Car's valde
$14,000
$12,000
$10,000
$8.000
$6,000
$4,000
$2,000
$0
20,000 40.000 60.000 80.000 100.000 120,000
Mileage

Can someone please help me..

Please need help thank

Please help.A teacher asked her pupils what their favourite school subject was.
PE
27
Maths
English
135
Science
3 pupils said PE was their favourite subject.
How many pupils said that Maths was their favourite subject?

The measures of the angles of a triangle are shown in the figure below. Solve for x.

13 The Lozano's chartered a boat over the holiday
weekend. The cost for the day was $350 plus the
6.5% sales tax. They also decided to tip their
guide 25% of the original cost of the boat rental.
What is the total amount they paid?

FIRST TO ANSWER GETS BRAINLIEST!!!
Find the y-intercept of the following line:
y=−8x+7