Appointments in a Medical Office Are Scheduled Every 15 Minutes

Essay

Appointments in a medical office are scheduled every 15 minutes. Throughout the day, appointments will be running on time or late, depending on the previous appointment only, according to the following matrix of transition probabilities: $$\begin{array} { c | c c } \text { Previous } & { \text { Next Appointment } } \\\text { Appointment } & \text { On Time } & \text { Late } \\\hline \text { On Time } & .75 & .25 \\\text { Late } & .30 & .70\end{array}$$
a.The day begins with the first appointment on time.What are the state probabilities for periods 1, 2, 3 and 4?
b.What are the steady state probabilities?