Patients arrive independently at a health clinic in regional Australia to visit one of two doctors, Patients arrive to see Dr Florence Nightingale according to a Poisson process at a rate of three per hour, and arrive to see Dr Carl Gauss according to a Poisson process at a rate of two per hour. Patients arrive to see Dr Nightingale independently of those that arrive to see Dr Gauss. The clinic is only open for 3 hours a day, from 1lam until 2pm and patients only arrive during the opening times. (a) Given that six patients arrived in total during the first hour the clinic was open, what is the probability that exactly two patients arrived in total between 1pm and 2pm? (b) On a different day, exactly two patients arrived between 11am and 12pm. What is the probability that both patients arrived to see Dr Nightingale