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Two percent of the population has a certain condition for which there are two diagnostic tests. Test A, which costs $1 per person, gives positive results for 80% of persons with the condition and for 5% of persons without the condition. Test B, which costs 100$ per person, gives positive results for all persons with the condition and negative results for all persons without it. (a) Suppose that test B is given to 150 persons, at a cost of 15,000$. How many cases of the condition would one expect to detect? (b) Suppose that 2000 persons are given test A, and then only those who test positive are given test B. Show that the expected cost is $15,000 but that the expected number of cases detected is much larger than in part (a). |
