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

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 2% of all healthy people as having the serious disease. Suppose also that it incorrectly diagnoses 10% of all people having another minor disease as having the serious disease. It is known that 5% of the population has the serious disease, 5% has the minor disease, and 90% of population is healthy. Find the probability that a person selected at random really has serious disease if the test indicates that he or she does. as s

Explanation / Answer

probability that test diagnoses =P( have disease and correctly diagnose+healthy and incorrectly diagnose+minor disease and incorrectly diagnose) =0.05*0.95+0.90*0.02+0.05*0.10=0.0705

hence probability that person selected has serious disease given test indicates so

=P( have disease and correctly diagnose)/P( test diagnoses)=0.05*0.95/0.0705=0.673759

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