Assumed that 2% of the population in a city are infected by COVID-19. It is also assumed that from those who are infected took the PCR swab test, there is a 99% chance that the test will return a "positive" reading.Keep in mind that these tests are not perfect. Even if the suspect does not have COVID-19, there is some probability that the test will return a positive. Let's suppose that, given that an individual is not infected by COVID-19, there is still a 3% chance that the swab test will return a positive (and the suspect has to be quarantined).

a.Use a tree diagram to list the sample space for showing all possible outcomes after selecting a suspect (who either has COVID-19 or does not) and then testing (and the test will be either positive or negative). (5 points)

b.Calculate the probability that the suspect does not have COVID-19. (5 points)

c.What is the probability that the suspect has test positive, given that the suspect does not have COVID-19? (5 points)

d.What is the probability that a randomly chosen suspect will be COVID-19-free and will still test positive for COVID-19? (5 points)

e.Suppose the suspect has test negative. What is the probability that the suspect has COVID-19? (5 points)