.

  We define D+ as the event a randomly selected person is positive for the disease of interest, and T+ the event the person tests positive. The events D- and T- are the corresponding complementary events of negative for disease and testing negative, respectively.

Suppose that the prevalence is given by

$$P(D+) \; = \; .25 .$$

Suppose that the sensitivity of the test is

$$P(T+\vert D+) \; = \; .8 ,$$

and the specificity is

$$P(T-\vert D-) \; = \; .4 .$$

(a) Compute the positive predictive power P(D+|T+).

(b) Compute the negative predictive power P(D-|T-).