Bayes’ probability III. TB Screening. Suppose that if a person with tuberculosis

Question

Bayes’ probability III. TB Screening. Suppose that if a person with tuberculosis is given a TB screening, the probability that his or her condition will be detected is 0.90. If a person without tuberculosis is given TB screening, the probability that he or she will be diagnosed incorrectly as having tuberculosis is 0.3. Suppose, further, that 11% of the adult residents of a certain city have tuberculosis. If one of these adults is diagnosed as having tuberculosis based on the screening, what is the probability that he or she actually has tuberculosis? Interpret your result.

Explanation / Answer

what is the probability that he or she actually has tuberculosis?

P ( has turbeculosis / diagnosed as having tuberculosis based on the screening )

P( diagnosed as having tuberculosis based on the screening) = 0.11 * 0.90 + (1-0.11) * 0.3 = 0.333

P( has turbeculosis / diagnosed as having tuberculosis based on the screening) = 0.11*0.90 / 0.333 = 0.297

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