One of the things graduating engineers fear most about their first job assignment is the required urinalysis test to screen for the use of illicit substances (THC, cocaine, opiates). USA Today reports that such tests have "false positive" rates (that is, they identify non-users as users) about 15% of the time. Presumably, the rate for "false negatives" (where users are identified as non-users) is lower, perhaps around 10%. Assume that 3% of students are users of illicit substances at the time they are screened via urinalysis.

a. What is the unconditional probability that a student selected at random will test positive for illicit substances ?

b. Suppose an individual selected at random tests positive for illicit substances. What is the probability that this person is actually not a user ?

c. An individual selected at random tests negative for illicit substances. What is the probability that he/she actually is a user ?

d.What is the probability that an individual who does not use drugs will get a positive reading on two consecutive tests ?