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
kompoz [17]
3 years ago
11

A new test to detect TB has been designed. It is estimated that 88% of people taking this test have the disease. The test detect

s the disease in 97% of those who have the disease. The test does not detect the disease in 99% of those who do not have the disease.
If a person taking the test is chosen at random, what is the probability of the test indicating that the person does not have the disease?

a) 0.1452b) 0.9900c) 0.0100d) 0.0300e) 0.0264f) None of the above.
Mathematics
1 answer:
Elodia [21]3 years ago
4 0

Answer:

Correct option: (a) 0.1452

Step-by-step explanation:

The new test designed for detecting TB is being analysed.

Denote the events as follows:

<em>D</em> = a person has the disease

<em>X</em> = the test is positive.

The information provided is:

P(D)=0.88\\P(X|D)=0.97\\P(X^{c}|D^{c})=0.99

Compute the probability that a person does not have the disease as follows:

P(D^{c})=1-P(D)=1-0.88=0.12

The probability of a person not having the disease is 0.12.

Compute the probability that a randomly selected person is tested negative but does have the disease as follows:

P(X^{c}\cap D)=P(X^{c}|D)P(D)\\=[1-P(X|D)]\times P(D)\\=[1-0.97]\times 0.88\\=0.03\times 0.88\\=0.0264

Compute the probability that a randomly selected person is tested negative but does not have the disease as follows:

P(X^{c}\cap D^{c})=P(X^{c}|D^{c})P(D^{c})\\=[1-P(X|D)]\times{1- P(D)]\\=0.99\times 0.12\\=0.1188

Compute the probability that a randomly selected person is tested negative  as follows:

P(X^{c})=P(X^{c}\cap D)+P(X^{c}\cap D^{c})

           =0.0264+0.1188\\=0.1452

Thus, the probability of the test indicating that the person does not have the disease is 0.1452.

You might be interested in
Does it lie inside, outside, or on the circle?​
FrozenT [24]

Answer:

<u>Given circle:</u>

  • (x - 4)² + y² = 25

The center is at (4, 0) and the radius is 5 units

<u>Lets find the distance from (7, 2) to the center of the circle:</u>

  • <u />d = \sqrt{(7 - 4)^2 + (2 - 0)^2}  = \sqrt{9+4} = \sqrt{13} < 5

Since d < 5, the point (7, 2) lies <u>inside</u> the circle

8 0
3 years ago
If x : 3 = 5 : 7 , then x = ………
Veronika [31]

Answer:

the answer is A which 2(1/7)

5 0
2 years ago
Does 8,6,4 contain numbers that are less than 10
raketka [301]
Yessssssssssssssssss
6 0
3 years ago
Which fraction is equivalent to 15/30<br> A 3/4<br> B 2/4<br> C 3/5<br> D 5/6
Ratling [72]

Answer:

2/4

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Using the greatest common factor for the terms, how can you write 56 + 32 as a product?
WARRIOR [948]
The answer is c ...use the distrubutive property to check it
8 0
3 years ago
Other questions:
  • Given A25=176 and the common difference of the arithmetic is 8, find a52.
    14·1 answer
  • What is the mean of a random variable that is uniformly distributed in [1/2,1] interval?
    7·1 answer
  • Which models can be used to solve the problem
    5·2 answers
  • PLZZ HELP MEEEEEEEEE
    14·2 answers
  • Select the correct anwser from the drop down menu.
    10·2 answers
  • 90% of 60,000,000 <br><br> Please help soon
    9·2 answers
  • Help Please Slope!!!!
    6·2 answers
  • If the crane operator works 30 years and the train engineer works 33 years, who makes the most lifetime income? How much more?
    12·1 answer
  • The distance between two rivers on a city map is 8. 5 centimeters. The scale on the map states that 3 centimeters represents 6 k
    12·1 answer
  • Find sin(x/2), cos (x/2), and tan(x/2) from the given information.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!