. In a study considering risk factors for HIV infection among intravenous drug users, it was found that among so-called light IV drug usersi.e. those with 100 or fewer injections per monththe rate of HIV seropositivity was 0.3. Among the so-called heavy drug usersi.e. those with strictly more than 100 injections per monththe rate of HIV seropositivity was 0.5. Assume that the HIV status of different people are independent. Answer the following questions.(a) What is the probability that exactly 3 of 5 light users are HIV positive?(b) What is the probability that at least 2 of 5 light users is HIV positive?(c) Suppose we have a group of 10 light users and 10 heavy users. What is the probability that exactly 6of the 20 users are HIV positive? Is the distribution of the number of HIV positive among the twenty users binomial? Why or why not?