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. Represent the "74.6%" using notation.
O P(S)
O P(S and POS)
O P(POS)
O P(POS I S)

Answer 1

Answer:

P(POS/S)

Explanation:

Here, P(S) represents the probability that the adult really has tuberculosis,

P(S and POS) represents the probability that the adult really has tuberculosis and the test gives a positive result.

P(POS) represents the probability the test gives a positive result.

Finally, P(POS/S) represents the probability that the test correctly identifies adults with tuberculosis, which is exactly 74.6%.