The state medical school has discovered a new test for tuberculosis. Experimentation with this new test has shown that the probability of a positive test result for tuberculosis when a person actually has it is 0.82. The probability of a false positive test result is 0.09. It is presumed that 4% of the population has tuberculosis. If a person is chosen at random, what is the probability that he/she a.) has tuberculosis and a positive test? b.) has a positive test and does not have tuberculosis? c,) tests negative for tuberculosis?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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The state medical school has discovered a new test for tuberculosis. Experimentation with this new test has shown that the probability of a positive test result for tuberculosis when a person actually has it is 0.82. The probability of a false positive test result is 0.09. It is presumed that 4% of the population has tuberculosis. If a person is chosen at random, what is the probability that he/she

a.) has tuberculosis and a positive test?

b.) has a positive test and does not have tuberculosis?

c,) tests negative for tuberculosis?

 

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