5. 2,117 randomly chosen people are cross-classified by sex and whether they are HIV positive or HIV negative. The results are in the table below.

	Female	Male
HIV Positive	17	100
HIV Negative	400	1600

1. If one person is chosen at random from these 2117, find the following probabilities.

1. P( Female and HIV Positive )

1. P( HIV Positive | Female )

1. P( HIV Positive | Male )

1. Are sex and HIV status independent? Make sure to justify your answer.

1. Suppose we select 3 people, without replacement, at random from these 2117 people. Find the probability that they are all HIV negative.