how can i solve this q as can as possible

In an airport in a Scandinavian country, health care professionals randomly test people for COVID-19. Suppose that the test kit used has a 0.95 probability of detecting COVID-19 if the person is infected. Moreover, suppose that the test gives a 0.99 probability of not detecting COVID-19 if the person is not infected. Assume that 10 percent of people who pass the airport are infected with COVID-19. (a.) (2 marks) Suppose that a person returns a negative test result. What is the probability that the person is not infected?Suppose that a person returns a positive test result. What is the probability that the person is infected? (c.) (4 marks) What is the probability that a test results in a positive test result? (d.) (4 marks) Health care professionals randomly select 17 people for testing. What is the probability that between 2 to 4 of them have COVID-19? What is the probability that at least 13 of them do not have COVID-19? Carefully state your assumptions. (e.) (4 marks) Suppose that 6 out of the 17 people tested in (d.) are men, and that 11 of them are women. Suppose that a second test is carried out, where 4 out of the 17 people are randomly sampled to undergo a second round of testing. What is the probability distribution of the number of men among the 4 persons who undergo the second round of testing? Clearly state the probability distribution and its parameters. (f.) (4 marks) Ramona works in a lunch restaurant at the airport. What is the probability that she has to serve at least three people before she encounters the first COVID-19 infected person? What is the probability that the 8th person she serves is the second one who has a COVID-19 infection