(3) Alan Cooper’s answer to Alice and Bob flip a biased coin, best $n$ out of $2n-1$ win. If the probability of Alice winning a flip is $p$, what is her chance of winning the series? – Quora

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Since this is tagged with “Puzzles and Trick Questions” it may be that I am missing something. But my answer would be $\Sigma_{m=0}^{n-1}p^{2n-1-m}(1-p)^m$ .

This follows the pattern of the best 2 out of 3 case where Alice has to win either two or three games – which happens in cases lww,wlw,wwl or www with probability $3p^2(1–p)+p^3=3p^2–2p^3$ (where the fact that the game may be stopped when she wins twice just corresponds to the fact that $pp(1-p)+ppp=p^2$ , and the same answer is obtained by taking the complement of the cases where Bob wins either 2 or 3 games).