Devin has N umbrellas that he uses walking from home to work. Some of the umbrellas are at home and some are at work at any point.He only takes the umbrella with him if its raining, which occurs with probability p independently. Devin is at home at t=0, and after each time step, Devin travels to another location and takes his umbrella with him if its raining and one is available at his location. If all umbrellas are at one location while Ben is at the other and it rains, then Devin gets wet.

a) Generalize the Markov chain to where Devin has N umbrellas.

b) Using MATLAB or Python, simulate the system for N = 4, p = 0.6, up to t = 1000 if a) all umbrellas start at Ben's home, and b) Umbrellas are initially evenly split. Compare the probability that Devin gets wit in these two simulations.

c) Determine the probability that Devin gets wet given that N= 4 and p = 0.6.