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.

a. P(S and POS)

b. P(POS)

c. P(POS | S)

d. P(S)

e. P(S | POS)