Question

Tests for tuberculosis like all other diagnostic tests are not perfect. Qft-g is one of such tests for tuberculosis. Suppose that for the population of adults that is taking the test, 5% have tuberculosis. The test correctly identifies 74. 6% of the time adults with a tuberculosis and correctly identifies those without tuberculosis 76. 53% of the time. Suppose that pos stands for the test gives a positive result and s means that the adult really has tuberculosis. What is the probability of an adult getting a neg result and truly not having tuberculosis?.

Answer 1

Based on the various probabilities, the probability of the above happening is 72.7%.

Probability of not having tuberculosis

= 1 - probability of having Tuberculosis

= 1 - 5%

= 95%

Probability of getting a negative result without tuberculosis

= Probability of not having tuberculosis x Probability that test result is accurate about not having tuberculosis

= 95% x 76.53%

= 0.727035

= 72.7%

In conclusion, this is 72.7%.

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