The state medical school has discovered a new test for tuberculosis. (If the tes

Question

The state medical school has discovered a new test for tuberculosis. (If the test indicates a person has tuberculosis, the test is positive.) Experimentation has shown that the probability of a positive test is 0.78, given that a person has tuberculosis. The probability is 0.05 that the test registers positive, given that the person does not have tuberculosis. Assume that in the general population, the probability that a person has tuberculosis is 0.05. What is the probability that a person chosen at random will fall in the following categories. (Enter your answers to four decimal places.)

(a) have tuberculosis and have a positive test

(b) not have tuberculosis

(c) not have tuberculosis and have a positive test

Explanation / Answer

(a) have tuberculosis and have a positive test:
0.05*0.83 = 0.0415 <-----

(b) not have tuberculosis:
1 - 0.05 = 0.95 <-----

(c) not have tuberculosis and have a positive test:
0.95*0.09 = 0.0855 <-----

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