In a recent column in Parade magazine, Marilyn Vos Savant raised the following question:
Suppose we assume that 5%of people are drug-users. A test is 95%accurate, which we'll say means that if a person is a user, the result is positive 95%of the time; and if she or he isn't, it's negative 95%of the time. A randomly chosen person tests positive. Is the individual highly likely to be a drug-user?
Marilyn's answer was:
Given your conditions, once the person has tested positive, you may as well flip a coin to determine whether she or he is a drug-user. The chances are only 50-50. But the assumptions, the makeup of the test group and true accuracy of the tests themselves are additional considerations.
As reported in CHANCE magazine, in June of 1987 (former) Secretary of Health and Human Services Otis Bowen suggested taking blood samples from 45,000 randomly selected Americans and testing for the presence of HIV antibodies.
Read Part I of FPPA (Chapter 1 and 2) and do review exercises 2,4,5,7,8,10,11 at the end of Chapter 2.