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.

- How can Marilyn's answer be correct?
- What does she mean by saying that the makeup of the test
group is an additional consideration?

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.

- Suppose that if a person has the antibodies, the probability
of a positive test is 99.9%, and that if the person does not
have the antibodies the probability of a negative test is
99%. Assume that 1.5 million out of 250 million Americans
have HIV antibodies. If a subject tests positive for the HIV
antibodies, what is the probability that he or she actually
has HIV antibodies.
- Should there be mandatory HIV testing? For whom?

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.

Tue Jun 28 15:24:59 EDT 1994