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.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.7: Probability
Problem 1SE: What term is used to express the likelihood of an event occurring? Are there restrictions on its...
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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.
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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