Question: Alice roll a fair 6 sided dice until she gets an ordered sequence of {4,5,5,2} in recent 4 rounds. (1) What is the probability of

Alice roll a fair 6 sided dice until she gets an ordered sequence of {4,5,5,2} in recent 4 rounds. (1) What is the probability of she stopping at round n? Justify your answer. (2) What is the expected value of the number of total rounds? (3) What is the expected value if the number of total rounds is less than equal to 8

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