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