An individual possesses umbrellas, which she employs in going from her home to office and vice versa If she is at home (the office) at the beginning (end) of a day and it is raining, then she will take an umbrella with her to the office (home), provided there is one to be taken. If it is not raining, then she never takes an umbrella Assume that, independent of the past, it rains at the beginning (end) of a day with probability p.

(a) Define a Markov chain with r + 1 states that will help us determine the proportion of time that our individual gets wet. (Note: She gets wet if it is raining and all umbrellas are at her other location.)

(b) Compute the limiting probabilities.

(c) What fraction of time does the individual become wet?