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?