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We play a game where we throw a coin at most 4 times. If we get...

We play a game where we throw a coin at most 4 times. If we get 2 heads at any point, then we win the game. If we do not get 2 heads after 4 tosses, then we loose the game. For example, HT H, is a winning case, while T HT T is a losing one. We define an indicator random variable X as the win from this game.

You make a decision that after you loose 3 times, not necessarily consecutively but overall, then you quit playing. On average, how many times you will play this game before quitting?

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