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There are quite a few topics on this question already but I couldn't find a well-explained solution. Please point me towards some relevant literature or theory to analyze this problem.

$K$ consecutive heads with a biased coin?

Probability of tossing a biased coin without having k heads consecutively in a row

Probability of tossing a fair coin with at least $k$ consecutive heads


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I think this would be a duplicate except that you're asking for relevant literature or theory; as such I've added the reference-request tag. – 6005 Sep 12 '13 at 17:51
"I couldn't find a well-explained solution" Users Sasha and joriki will be delighted. (Unrelated: several other MSE pages answer the same question in details.) – Did Sep 12 '13 at 17:59
Feller, "An Introduction to Probability Theory and Its Applications, Volume 1, 3rd Edition", section XIII.7. – awkward Sep 12 '13 at 23:06

There are at least two methods that can solve this problem. Both are discussed in detail in this question:

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