The number of patients get tested at a COVID-19 drive through test site follows a Poisson process with parameter ? = 4 per minute. Suppose the probability that a patient is tested positive for COVID is p = 0.9. a) Find the probability that no patients get tested in 30 seconds. (2 marks) b) Find the distribution of the number of patients that are tested positive in ` minutes. (5 marks) c) Find the probability that the first patient is tested positive shows up at least 1 minute after the test center opens. (3 marks)

Question 2 The number of patients get tested at a COVID-19 drive through test site follows a Poisson process with parameter A = 4 per minute. Suppose the probability that a patient is tested positive for COVID is p = 0.9. it) Find the probability that no patients get tested in 30 seconds. (2 marks ) b) Find the distribution of the number of patients that are tested positive in 6 minutes. (5 marks) 0) Find the probability that the rst patient is tested positive shows up at least 1 minute after the test center opens