3. [10 marks] In a particular city, 15% of people are infected with a virus and an antigen test is available for detecting infection. Using this test, 20% of people who are infected will test negative (this is the false negative rate), and 95% of people who are not infected will test negative (specificity). Let I be the event that a randomly selected person is infected and let N be the event that a randomly selected person tests negative using the antigen test. (a) Using the given information, write down P(I), P(N|I), and P(N|I). Questions continue on the next page. (b) Find the probability that a person is infected and tests negative. (c) Find the probability that a person is not infected and tests negative. (d) Hence calculate the probability that a person tests negative. (e) Now calculate the probability that a person is actually infected given that they have returned a negative test.