2. Suppose there is a newly developed drug test for an illegal drug. Further suppose the test is 97% accurate in the case of a user of that drug (it produces a positive result with probability .97 in the case that the tested individual uses the drug) and 70% accurate in the case of a non-user (it is negative with probability .7 in the case the person does not use the drug). Suppose it is known that 15% of the entire population uses this drug.

(a) Suppose that a randomly selected individual tested negative for drug use. What is the probability that this individual uses the illegal drug? Explain your answer very carefully.

(b) Suppose that a randomly selected individual tested positive for the drug use. What is the probability that individual does not use the drug? Explain your answer very carefully.