Oliver Undergoes a Standard Medical Test While at His Regular

Essay

Oliver undergoes a standard medical test while at his regular checkup. The test is 90% reliable in detecting a form of cancer (C) that is found in 2% of the population. In particular, Pr(+|C) = .90. The test is also 90% reliable in screening out cancer, that is, Pr(-|H) = .90.
(a) If Oliver tests positive, how likely is it that he actually has cancer? If he tests negative, what is his cancer risk?
(b) Persons who test negative, and who actually have cancer, are able to sue for malpractice. Plaintiffs in such legal suits are awarded $250,000 on average (to cover medical expenses, pain and suffering, and legal fees). What is the hospital’s expected monetary liability due to the risk of incorrect negative tests?