In: Statistics and Probability
. A certain blood test comes back positive 90% of the time for patients having a certain disease, but the test also comes back positive 20% of the time in healthy people. In a certain location 30% of the people have the disease, and anybody with a positive blood test is given a drug that cures the disease. If 25% of the time drug produces a characteristic rash, what is the probability that a person from this location who has the rash had the disease in the first place?