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Exercise 2 We have a biased coin that lands on tails 1/3 of the time and heads 2/3 of the time. We toss it until

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Exercise 2 We have a biased coin that lands on tails 1/3 of the time and heads 2/3 of the time. We toss it until we get a sequence of 2 consecutive heads or a sequence of 2 consecutive tails. What is the probability of getting 2 consecutive heads before 2 consecutive tails? (Hint: We can condition on the first toss)

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