A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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A certain affects virus 0.3% of the population. A test used to detect the virus in a person is positive 90% of
the time if the person has the virus (true positive) and 15% of the time if the person does not have the virus
(false postive). Fill out the remainder of the following table and use it to answer the two questions below.
Total
Infected
Not Infected
Positive Test
Negative Test
Total
300
99,700
100,000
a) Find the probability that a person has the virus given that they have tested positive. Round your answer
to the nearest tenth of a percent and do not include a percent sign.
P(Infected | Positive Test)=
b) Find the probability that a person does not have the virus given that they test negative. Round your
answer to the nearest tenth of a percent and do not include a percent sign.
P(Not Infected | Negative Test) =
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Transcribed Image Text:A certain affects virus 0.3% of the population. A test used to detect the virus in a person is positive 90% of the time if the person has the virus (true positive) and 15% of the time if the person does not have the virus (false postive). Fill out the remainder of the following table and use it to answer the two questions below. Total Infected Not Infected Positive Test Negative Test Total 300 99,700 100,000 a) Find the probability that a person has the virus given that they have tested positive. Round your answer to the nearest tenth of a percent and do not include a percent sign. P(Infected | Positive Test)= b) Find the probability that a person does not have the virus given that they test negative. Round your answer to the nearest tenth of a percent and do not include a percent sign. P(Not Infected | Negative Test) =
Expert Solution
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Step 1

Let X represent that the person has the disease

A represent that the test is positive

B represent that the test is negative

Then it is given that:

PA|X=0.9PA|X'=0.15

Total number of people = 100,000

The completed table is thus:

InfectedNot infectedTotalPositive test0.9×300=2700.15×99700=1495515225Negative test0.1×300=300.85×99700=8474584775Total30099700100,000

 

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