There are 550,000 people in the US infected with HIV. Of these people, 275,000 are drug users, and the rest are not drug users. The total population of the US is 250 million. There are 10 million drug users in the US.

The standard blood test for HIV infection is not always accurate. The probability that someone who is infected with HIV will test positive for HIV is 0.99. The probability that someone who is not infected with HIV will test negative for HIV is also 0.99.

Suppose that a randomly chosen person takes the standard blood test for HIV, and the outcome of the test is positive. What is the probability that this person is infected with HIV?

Suppose that a randomly chosen drug user takes the standard blood test for HIV, and the outcome of the test is positive? What is the probability that this person is infected with HIV?