A diagnostic test for a disease is said to be 90% accurate inthat if a person has the disease, the test will detect it withprobability 0.9. Also, if a person does not have the disease, thetest will report that he or she does noot have it with probability0.9. Only 1% of the population has the disease in question. If aperson is chosen at random from the population and the diagnostictest indicates that she has the disease, what is the conditionalprobability that she does, in fact, have the disease? Are yousurprised by the answer? Would you call this diagnostic testreliable?
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