The ELISA is a test to determine whether the HIV antibody is present. The test is 99.5% effective, which means that the test will come back negative if the HIV antibody is not present 99.5% of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is 0.005. Suppose that the ELISA is given to ﬁve randomly selected people who do not have the HIV antibody.
(a) What is the probability that the ELISA comes back negative for all ﬁve people?
(b) What is the probability that the ELISA comes back positive for at least one of the ﬁve people?