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

Question

2. Suppose a test for a serious disease is successful in detecting the disease in 95% 11 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, 8% 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.

Explanation / Answer

P(Serious disease/Test indicate that he/she does)

= (0.02*0.95)(0.02*0.95+0.90*0.04+0.08*0.12)

= 0.019/0.0646

= 0.2941 ( rounded to four decimal places)

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