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Expected number of questions to win a game

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Expected number of questions to win a game

Let, a person is taking part in a quiz competition. For each questions, there are 3 answers, and for each correct answer he gets 1 point. When he gets 5 points, he wins the game. If he gives 4 consecutive wrong answers, then his points resets to zero (i.e. if his score is now 4 and he gives 2 wrong answers, then his score resets to 0).

My question is, on an average how much questions he needs to answer to win the game?


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