A drug test for college athletes will result in three possible test results: Positive, Negative or Inconclusive. For a drug user the probability of these outcomes is 0.65, 0.06 and 0.29 respectively. For a nonuser these probabilities are 0.03, 0.72, and 0.25. The prior probability of being a drug user is 5 %.
i) Compute the posterior probability that an athlete is a drug user given that her test results are positive, negative and inconclusive.
ii) What is the probability of observing a positive test result, a negative test result and an inconclusive test result?