Tests for Low Prevalence Diseases (p11)

Suppose that 5% of a given population has a disease that is difficult to detect. Call the state where the person has the disease D and the state where they don't have it N. A test for the disease is available that reports rD or rN for whether or not the person has the disease. However, it's imperfect: if the person has the disease (D), there is a 10% chance it will report they don't have it, rN. In addition, there's also a 10% chance that it will report that a person who doesn't have the disease (N) has it, rD.

1. What percent of reports of the disease, rD, are false positives? That is, what is the probability of N given rD or Pr(N|rD)?
2. What percent of the reports that the person doesn't have the disease, rN, are false negatives? That is, what is the probability of D given rN or Pr(D|rN)?
3. How many people in a population of 100,000 will be undertreated? Overtreated?