Every Week a Charter Plane Brings a Group of High-Stakes

Short Answer

Every week a charter plane brings a group of high-stakes gamblers into Las Begas.Half the group stays and begins gambling at Hot Slots near the Strip, and the other half is housed and begins gambling at Better Bandits, some distance away.(Both hotel/casinos are owned by the same corporation.)Once an hour, dedicated shuttle buses will transport to the other
casino any of the group members who wish to try their luck at the other casino.The transition probabilities are as follows:
$\begin{array}{c}\text { Next Hour }\\\begin{array}{lcc} &\text { Hot Slots }&\text { Better Bandits }\\\text{This Hot Slots} & .8&.2 & \\\text{Hour Better Bandits} & .3 & .7\end{array}\end{array}$

A.After three hours, what proportion of these gamblers are in the Hot Slots Casino?
B.What is the long run average percentage of these gamblers who
will be at Hot Slots Casino?