The state medical school has discovered a new test for tuberculosis. Experimenta

Question

The state medical school has discovered a new test for tuberculosis. Experimentation has shown that the probability of a positive test is 0.80, given that a person has tuberculosis. The probability is 0.06 that the test registers positive, given that the person does not have tuberculosis. Assume that in the general popular the probability that a person has tuberculosis is 0.04. What is the probability that a person chosen at random will fall in the following categories. have tuberculosis and have a positive test not have tuberculosis not have tuberculosis and have a positive test

Explanation / Answer

(a) P[have tuberculosis and have a positive test]

We have given ,

Assume that in the general population, the probability that a person has tuberculosis is 0.04.

and also,  Experimentation has shown that the probability of a positive test is 0.80, given that a person has tuberculosis.
0.04*0.80 = 0.032

(b) P[not have tuberculosis]

We have , the probability that a person has tuberculosis is 0.04.
1 - 0.04 = 0.96
(c) P[not have tuberculosis and have a positive test]

We have given , The probability is 0.06 that the test registers positive, given that the person does not have tuberculosis.
0.96*0.06 = 0.0576

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