5. 4,458 randomly chosen people are cross-classified by race, sex, and whether they are HIV positive or HIV negative. The results are in the tables below.

Race = 1 Female Male HIV Positive 17 100 HIV Negative 400 1600

Race = 2

Female Male HIV Positive 11 130 HIV Negative 450 1750

a) If one person is chosen at random from these 4458, find the following probabilities.

i. P( Female and HIV Positive )

ii. P( HIV Positive and Female | Race=1)

iii. P( HIV Positive | Male and Race=2)

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

c) Suppose we select 3 people, without replacement, at random from these 4458 people. Find the probability that they are all HIV negative males.