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I've been practicing my probability and trying to answer the question "how many times do you expect to flip a coin before n consecutive heads" and while I can follow many of the answers out there, I'm struggling to get my head around how you define all possible cases.

Specifically, I'm thinking about this solution: https://math.stackexchange.com/a/455568/653973 which covers all possibilities with two cases: flipping n - 1 heads and then a tail, or flipping n heads. Why do we not need to account for other cases, like flipping n - 2 heads followed by a tail?

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  • $\begingroup$ No, the ... in the answer means that the other cases are handled similarly. He is considering all the cases you mention. That is how he develops the formula. $\endgroup$ – saulspatz Mar 13 at 22:25

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