Suppose we are studying a test for a rare disease which is present in .5% of people (probability .005). If a person has the disease, the test will detect it 90% of the time (true positive rate). If a person does not have the disease, the test will detect it 95% of the time (true negative rate). (a) What is the probability that a person with a positive test result has the disease? (b) How high does the true negative rate have to be before the probability in part (a) is ? (c) Repeat parts (a) and (b), but assume the disease is much more common, and is present in 10% of people.
Suppose we are studying a test for a rare disease which is present in .5% of people (probability .005). If a person has the disease, the test will detect it 90% of the time (true positive rate). If a person does not have the disease, the test will detect it 95% of the time (true negative rate). (a) What is the probability that a person with a positive test result has the disease? (b) How high does the true negative rate have to be before the probability in part (a) is ? (c) Repeat parts (a) and (b), but assume the disease is much more common, and is present in 10% of people.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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![Suppose we are studying a test for a rare disease which is present in .5% of people (probability .005).
If a person has the disease, the test will detect it 90% of the time (true positive rate).
If a person does not have the disease, the test will detect it 95% of the time (true negative rate).
(a) What is the probability that a person with a positive test result has the disease?
(b) How high does the true negative rate have to be before the probability in part (a) is ?
(c) Repeat parts (a) and (b), but assume the disease is much more common, and is present in 10%
of people.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F320dac9a-afc1-457d-89c1-3729cdbfce4d%2Ff96c2857-b1d9-4262-a140-4922f471f571%2Fzsufj0e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose we are studying a test for a rare disease which is present in .5% of people (probability .005).
If a person has the disease, the test will detect it 90% of the time (true positive rate).
If a person does not have the disease, the test will detect it 95% of the time (true negative rate).
(a) What is the probability that a person with a positive test result has the disease?
(b) How high does the true negative rate have to be before the probability in part (a) is ?
(c) Repeat parts (a) and (b), but assume the disease is much more common, and is present in 10%
of people.
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