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 0.16. If the patient does not have the virus, the probability that the test indicates a (false) positive is 0.14. Assume that 5% 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.

b : this patient does not test negative. Show all your work. [2 marks]

c: Test to see if the events "tests positive" and "has the virus" are independent events. Show all your work.[2 marks]