Drug testing problem for conditional probability

August 30, 2017

Question
Drug testing problem for conditional probability
Suppose that a drug test for an illegal drug is such that it is 99% accurate in the case of a user of that drug (e.g. it produces a positive result with probability .99 in the case that the tested individual uses the drug) and 95% accurate in the case of a non-user of the drug (e.g. it is negative with probability .95 in the case the person does not use the drug). Suppose it is known that 10% of the entire population uses this drug.
A. Make a Tree
B. You test someone and the test is positive. What is the probability that the tested individual uses this illegal drug?
C. What is the probability of a false positive with this test (e.g. the probability of obtaining a positive drug test given the person tested is a non-user)?
B. What is the probability of obtaining a false negative for this test (e.g. the probability that the test is negative, but the individual tested is a user)?

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