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

test result?

(c) What is the probability of having the disease given a positive test

result?