Question

Extra Credit: ELISA tests are used to screen donated blood for the presence of the AIDS virus. The test actually detects antibodies, substances that the body produces when the virus is present. When antibodies are present, ELISA is positive with probability about 0.997 and negative with probability about 0.003. When the blood tested is not contaminated with AIDS antibodies, ELISA gives a positive result with probability about 0.015 and a negative result with probability 0.985. (Because ELISA is designed to keep the AIDS virus out of the blood supply, the higher probability of 0.015 of a false positive is acceptable in exchange for the low probability 0.003 of failing to detect contaminated blood. These probabilities are approximate they do depend on the expertise of the particular lab doing the test.) Suppose that 1% of a large population carries the AIDS virus Suppose that a single person is selected at random from the U.S. population and is tested for the AIDS virus using the ELISA test. Let A denote the event that the person actually carries the AIDS virus, and let T denote the event that the person tests positive for the virus (whether or not the person actually carries AIDS) a. Describe in words what each of the following probabilities means, and then find the numerical value of each of these probabilities. (Hint: these values are all given directly in the problem; no computations are needed.) P(d), P(d'). P(T A), and P(T A.) b. Compute P(TnA) and P(Tn A c. Compute P(T), the total probability that the person will test positive for AIDS d. Are the events A and T independent? Clearly justify your answer with an appropriate computation. f. Would it be desirable for the events A and T to be independent? Clearly explain your answer! g. Given that the individual tests positive for AIDS, compute the conditional probability that the persorn actually carries the virus h. Is it surprising to you that the result in part (g) is so small? Try to explain why this probability is so small. Discuss some of the practical meaning of this result.

hi, my answers seemed strange after using Bayes theorem, so I am unsure if I made the right calculations. Please show your work so I can catch my error :)

Answer 1

Soluhon: P (T/A) 997 CLJ 0 01485 : o. 0 oo 2 48 2 000 1-0: 13