Ossian flees the mine once he learns his mother caught a strong form of the influenza virus. Immediately upon his return, he takes her to the regional government medical clinic. The process of seeing a doctor is as follows. All patients must be triaged before seeing a doctor. The lineups ahead of the triage nurse are notorious, one can see an average of 50 people waiting to be triaged. From there, patients can follow one of two paths: if they bribe the triage nurse there is a "fast track option" in an adjacent unlabeled building. If a patient cannot afford the bribe, they must stay in the official system. In both systems patients see doctors one-on-one.

The "bribe" option is well staffed by doctors, an average of 5 doctors are working and 80 per cent of the time they are seeing patients. Fast track patients spend an average of 10 minutes in consultation with a doctor before leaving the clinic.

The "no bribe" option is even more notorious than triage for long waits. They have a large waiting room which can fit up to 100 patients, which on average is 90 per cent full. An average wait before seeing a doctor in the "no bribe" option is 5 hours. In addition, patients in this option spend less time with a doctor once they are seen, an average of 6 minutes. Doctors in this option are overworked, seeing patients 90 per cent of the time they are working.

(a) On average, what percentage of patients bribe the triage nurse?

(b) What is the average wait before being triaged?

(c) How many more doctors on average are staffing the "bribe" option than the "no bribe" option?