Consider a company which has decided to implement a random illegal drug test policy for its employees. In this case it is in the best interests of both the company and their employees that any such test is reliable.
Suppose that 1.05% of all employees at the company are using illegal drugs and a further 0.04% use prescription drugs. Further suppose that the illegal drug test put in place is 98% ac-curate in the sense that it indicates a positive test result for illegal drugs 98% of the time when a person actually has illegal drugs in their system. However it also indicates a false positive 10% of the time when a person has prescription drugs in their system and 1.5% of the time if someone is not using any drugs.
(a) The sample *ace for this problem is 12 = { all employees in a company}. Define all four events given.

(b) Write down all the information given above in terms of probability statements. (You should have 5 statements.)

(c) What is the probability that a randomly chosen employee does not use any drugs?

(d) What is the probability that a randomly chosen employee tests negative for illegal drugs given that they actually have illegal drugs in their system?

(e) What is the probability that a randomly chosen employee tests positive for illegal drugs?

(f) If a randomly chosen employee tests positive for drugs what is the probability that they are actually using illegal drugs?

(g) What is the probability that a randomly chosen employee who tested negative for drugs is actually using illegal drugs?

(h) In the light of all the above information do consider this to be a reliable test? Why or why not?