A screening test for a certain virus is prone to giving false positives or false negatives. If a patient being tested has the virus, the probability that the test indicates a (false) negative is 0.12. If the patient does not have the virus, the probability that the test indicates a (false) positive is 0.15. Assume that 8 % of the patients being tested actually have the virus. Suppose that one patient is chosen at random and tested. Find the probability that:

Problem 9a. this patient does not have the virus and tests negative. Show all your work.

Problem 9b. this patient does not test negative. Show all your work

Problem 9c. Test to see if the events "tests positive" and "has the virus" are independent events. Show all your work.