Question: In Problem 4.7.9, it was assumed that every man had one son. Assume now that the probability that a man has a son is r.

In Problem 4.7.9, it was assumed that every man had one son. Assume now that the probability that a man has a son is r. Define a Markov chain with four states, where the first three states are as in Problem 4.7.9, and the fourth state is entered when a man has no son. This state cannot be left (it corresponds to a male line of the family dying out). Find the probability that an unskilled laborer has a grandson who is a professional man.

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