A disease is present in 2 out of every 1000 people. There is a test to determine whether you have the disease. If you have the disease, the test correctly comes back positive 85% of the time. If we ran the test on 1000 random people, on average 8 results would come back positive, and 992 results would come back negative.
(a) If you don't have the disease, what is the probability the test incorrectly comes back as positive?
(b) If the test comes back positive, what is the probability you have the disease?
(c) If the test comes back negative, what is the probability you don't have the disease? Provide justifications and citations for your responses.