A person owns a total of two umbrellas. The person regularly moves between their home and office. Each time step is a day; the person going from home to office and returning back home. They take along an umbrella only if it rains, otherwise all the umbrellas stay in place. There are times when both umbrellas are in one place, while the person is in the other place, so in that case if it is raining they get wet. Let p denote the probability that it is raining, so q = 1 − p is the probability it is not raining. 1. Write out the one-step state transition matrix in terms of p and q. 2. If the probability of rain p = 0.30, what is the probability that the person gets wet?
A person owns a total of two umbrellas. The person regularly moves between their home and office. Each
time step is a day; the person going from home to office and returning back home. They take along an
umbrella only if it rains, otherwise all the umbrellas stay in place. There are times when both umbrellas are
in one place, while the person is in the other place, so in that case if it is raining they get wet. Let p denote
the probability that it is raining, so q = 1 − p is the probability it is not raining.
1. Write out the one-step state transition matrix in terms of p and q.
2. If the probability of rain p = 0.30, what is the probability that the person gets wet?
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