As reported in 2010, Hawaii is the state with the highest rate of tuberculosis (TB), at 8.8 cases per 100,000 population, 1 for a probability of 0.000088. A relatively new, rapid TB test has a sensitivity of 0.98, meaning that's the probability of the test detecting TB in a patient who has TB, so only 0.02 of the people with TB end up with a false negative test result. 2 The false positive rate for this test (which is the probability of a positive test given that the person doesn't have TB) is 0.008. Use this information and the Bayes' Theorem equation to calculate what the probability is of a person living in Hawaii not having TB, given that the person had a positive test result when given this TB test. P(A|B) = P(A)*P(B|A) P(A)*P(B|A)+P(A)«P(B|A) where A= Event "not A." |
As reported in 2010, Hawaii is the state with the highest rate of tuberculosis (TB), at 8.8 cases per 100,000 population, 1 for a probability of 0.000088. A relatively new, rapid TB test has a sensitivity of 0.98, meaning that's the probability of the test detecting TB in a patient who has TB, so only 0.02 of the people with TB end up with a false negative test result. 2 The false positive rate for this test (which is the probability of a positive test given that the person doesn't have TB) is 0.008. Use this information and the Bayes' Theorem equation to calculate what the probability is of a person living in Hawaii not having TB, given that the person had a positive test result when given this TB test. P(A|B) = P(A)*P(B|A) P(A)*P(B|A)+P(A)«P(B|A) where A= Event "not A." |
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:As reported in 2010, Hawaii is the state with the highest rate of tuberculosis (TB), at 8.8 cases
per 100,000 population, 1 for a probability of 0.000088. A relatively new, rapid TB test has a
sensitivity of 0.98, meaning that's the probability of the test detecting TB in a patient who has
TB, so only 0.02 of the people with TB end up with a false negative test result. 2 The false
positive rate for this test (which is the probability of a positive test given that the person doesn't
have TB) is 0.008.
Use this information and the Bayes' Theorem equation to calculate what the probability is of a
person living in Hawaii not having TB, given that the person had a positive test result when
given this TB test.
P(A|B) = P(A)*P(B|A)
P(A)*P(B|A}+P(A)*P(B|A)
where A= Event "not A." |
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