and the observation test. What the patient is concerned about is P(disease|test). Roughly speaking,
the reason it is a good thing that the disease is rare is that P(disease|test) is proportional
to P(disease), so a lower prior for disease will mean a lower value for P(disease|test). Roughly
speaking, if 10,000 people take the test, we expect 1 to actually have the disease, and most likely
test positive, while the rest do not have the disease, but 1% of them (about 100 people) will test
positive anyway, so P(disease|test) will be about 1 in 100. More precisely, using the normalization
equation from page 428: