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 Jan 4 awarded Notable Question Aug 24 awarded Supporter Mar 25 awarded Popular Question Feb 24 awarded Student Feb 24 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? Feb 24 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! Feb 24 awarded Scholar Feb 24 accepted coin tossed until two consecutive heads or tails appear Feb 24 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 $P(H) = p$? Feb 24 awarded Editor Feb 24 revised coin tossed until two consecutive heads or tails appear added 45 characters in body Feb 24 asked coin tossed until two consecutive heads or tails appear