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 Jan4 awarded Notable Question Aug24 awarded Supporter Mar25 awarded Popular Question Feb24 awarded Student Feb24 comment coin tossed until two consecutive heads or tails appear @André: In your shorter solution, are you using a property like: if $X = f(Y)$, then $P(X = f(y)) = P(Y = y)$? If yes, why is it true? Is it true only for one-to-one functions? Feb24 comment coin tossed until two consecutive heads or tails appear @André: Separating the even and odd case was the trick here, I guess. I was completely stuck thinking how to write a common expression for the PMF. Thanks! Feb24 awarded Scholar Feb24 accepted coin tossed until two consecutive heads or tails appear Feb24 comment coin tossed until two consecutive heads or tails appear Edited the question. Thanks for the detailed solution. Any hints on how to generalize if $P(H) = p$? Feb24 awarded Editor Feb24 revised coin tossed until two consecutive heads or tails appear added 45 characters in body Feb24 asked coin tossed until two consecutive heads or tails appear