4. Suppose a test for a serious disease is successful in detecting the disease i

Question

4. Suppose a test for a serious disease is successful in detecting the disease in 95% of all persons infected but that it incorrectly diagnoses 4% of all healthy people as having the serious disease. Suppose also that it incorrectly diagnoses 12% of all people having another minor disease as having the serious disease. It is known that 2% of the population has the serious disease, 800 has the minor disease, and 90% of population is healthy. Find probability that the test indicates that a person selected at random has serious disease

Explanation / Answer

P(test indicates a serious disease)=P(have serious disease and test indicates a serious disease+haveminr disease and test indicates a serious disease+healthy and test indicates a serious disease)

=0.02*0.95+0.08*0.12+0.9*0.04=0.0646

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