A blood test is 99% effective in detecting a certain disease when the
disease is present. However, the test also yields a false positive result
for 2% of healthy patients tested. Suppose that 0.5% of the population
have the disease.
(a) What proportion of healthy patients are correctly diagnosed?
(b) What is the unconditional (or marginal) probability of a positive
(c) What is the probability of having the disease given a positive test