(hiv testing.) according to the centers for disease control and prevention, 1 in every 10,000 pre-screened volunteer blood donors in the united states is infected with the human immunodeficiency virus, or hiv. to reduce the chance of transmitting this virus to other individuals, each unit of donated blood is subject to an immunoassay test before the blood is used for trans- fusion. this test yields one of two possible outcomes: positive, which indi- cates that the blood donor has antibodies indicating the presence of hiv, or negative, which indicates that the donor does not have antibodies indicating the presence of hiv. the standard immunoassay test is not 100% accurate. on average, the test erroneously returns a negative test result for 1 in every 100 donors that are, in fact, infected with hiv. moreover, the test erroneously returns a positive test result for 1 in every 1000 donors that are, in fact, not in- fected with hiv. disclaimer: the numbers here are somewhat dated. (note: because of the small probabilities involved in this problem, carry out all in- termediate calculations to at least seven decimal places or, better yet, do all calculations in excel or stata.) (a) what is the probability that a unit of blood from a randomly selected pre-screened volunteer blood donor in the u. s. will test positive? (b) a unit of blood is tested, and the test result is positive. given this test re- sult, what is the probability that the donor does not actually have hiv?