I tried to got my my TA's office hours today but someone hogged him for 45 minutes and I didn't get a chance to ask my question. Hopefully someone can shed some light on this for me. Note that this is a question about diagnosing people with a disease $P(D)$ is the probability the person has the disease.
Assume that for a randomly selected person, $P(D) = 0.2$, $P(\text{Positive test}\mid D) = 1$. $P(\text{Positive test}\mid\overline{D}) = 0.05$, so that the inexpensive test only gives false positive, and not false negative results.
Suppose that this inexpensive test costs $\$10$. If a person tests positive then they are also given a more expensive test costing $\$100$, which correctly identifies all persons with the disease. What is the expected cost per person if a population is tested for the disease using the inexpensive test followed, if necessary, by the expensive test?