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A biased die is rolled until two 1s are rolled in succession, or until a 1 and then a 2 are rolled in succession

(in that order). The die lands on 1 with probability 50%, on 2 with probability 20%, and on something else with probability 30%. What is the probability that the rolling will end with successive 1s?

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As there are only two possible ways to end the rolling which considers the last 2 rolls so without any loss of generality we... View the full answer

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