9. [10 marks] One in 5000 individuals in a certain population has the human immunodeciency virus (HIV). A test for the virus is devised and the result of the test is either + or suggesting respectively the presence or absence of the virus. Clinical trials conrm the test to be 99% correct so that P[+ | H] = .99 = P[ | H 0] where H and HC represent respectively presence and absence of the virus. A) What is the probability that a person with HIV gets a negative response to the test. B) What is the probability that a person who gets a + on the test, has HIV. C) The 'false positive' situation is one in which a person who gets a + in the test is in fact HIV free. Calculate this probability and explain why it is so high