Wilson has two umbrellas, each of which could either be in his apartment or his office. Wilson walks from his apartment

[answerhappygod]

Wilson has two umbrellas, each of which could either be in his
apartment or his
office. Wilson walks from his apartment to his office; he also
walks from his office to his
apartment. Assume that on each of these walks:
•It rains with probability 0.5, independently of all other
walks.
•If it is not raining, Wilson ignores the umbrellas.
•If it is raining, he uses an umbrella if there is one, and gets
wet if there isn’t.
In the long run, what is the expected proportion of walks on which
Wilson gets wet?
(Hint: consider the number of umbrellas around Wilson and define a
Markov chain with
3 states.)