Two Airlines Offer Conveniently Scheduled Flights to the Airport Nearest

Essay

Two airlines offer conveniently scheduled flights to the airport nearest your corporate headquarters. Historically, flights have been scheduled as reflected in this transition matrix. $$\begin{array} { c | c c } \text { Current } & { \text { Next Flight } } \\\text { Flight } & \text { Airline A } & \text { Airline B } \\\hline \text { Airline A } & .6 & .4 \\\text { Airline B } & .2 & .8\end{array}$$
a.If your last flight was on B, what is the probability your next flight will be on A?
b.If your last flight was on B, what is the probability your second next flight will be on A?
c.What are the steady state probabilities?