Starting at 9 a.m., patients arrive at a doctor's office according to a Poisson process. On average, three patients arrive every hour. (a) Find the probability that at least two patients arrive by 9:30 a.m. (b) Find the probability that 10 patients arrive by noon and eight of them come to the office before 11 a.m. (c) If six patients arrive by 10 a.m., find the probability that only one patient arrives by 9:15 a.m.