The Senate is in the middle of a floor debate, and a filibuster is threatened. Senator Hanks, who is still vacillating, has a probability of .1 of changing his mind during the next 5 minutes. If this pattern continues for each 5 minutes that the debate continues and if a 24-hour filibuster takes place before a vote is taken, what is the probability that Senator Hanks will cast a yes vote? A no vote?

(A) Complete the following transition matrix:

(B) Find the stationary matrix and answer the two questions.

(C) What is the stationary matrix if the probability of Senator Hanks changing his mind (.1) is replaced with an arbitrary probability p?

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Current 5 minutes Next 5 minutes Yes No 1 Yes 9 No