Suppose you are tested to see if you have a rare disease. Assume that if you have the disease, your test will always come back positive, but if you do not have the disease, there is still a 0.001 chance that you will test positive. In reality, only 1 of 10,000 people have the disease. Your doctor calls and says that you have tested positive. He is sorry but there is a 99.9% (1-0.001) chance that you have the disease. Is he correct? What is the actual probability that you have the disease?