An urn contains five red and three green balls. The balls are chosen at random, one by one, from the urn. If a red ball is chosen, it is removed. Any green ball that is chosen is returned to the urn. the selection process continues until all of the red balls have been removed from the urn. What is the mean duration of the game?
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What is the probability for choosing one of the five red balls? What is the expected duration for this to happen for the first time? How does the situation change once a red ball has been removed? The total duration is the sum of the five individual durations for successively removing the red balls.