At an Emergency Room, one out of every four urgent patients triaged is followed by another urgent patient, while only one out of every five non-urgent patients is followed by an urgent patient.
(a) Derive a Markov chain model that represents the type of the patients who arrive to this emergency department. Be sure to define your states and one- step transition probability.
(b) What fraction of patients are urgent?
(c) Assume that patients are triaged on their order of arrival. If the fifth patient triaged is non-urgent, what is the probability that the seventh patient triaged is also non-urgent?