A certain disease has an incidence rate of 0.5%. If the false negative rate is 7% and the false positive rate is 2%, compute the probability that a person who tests positive actually has the disease.

Answer 1

A contingency table helps.
Complete the table

Test . has . . doesn't have
result disease disease
+ = 0.005*0.93 0.995*.02
- = 0.005*0.07 0.995*.98
tot. 0.005 0.995

The probability of a person who tests positive actually has the disease is in one of the cells.