A patient comes into the doctor saying that they don’t feel well. The patient’s symptoms perfectly match a bacterial infection that has struck 1% of the population. Before writing a prescription for the known cure, the doctor orders a test to see if the patient is infected. The test is very good, but not perfect – 1% of healthy patients will incorrectly register as positive. There is also a 1% chance that someone who is infected incorrectly registers as negative. Sure enough, the patient’s test comes back positive. Based only on the test, what are the chances that the patient is actually infected?
