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There are 26 steps in a staircase. You have a 51% chance to step onto the next step, and a 49% chance to step back down to the step prior. Assuming you are already on the first step, how many steps are you most likely to take to before stepping onto the 26th step?

jameselmore
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Tristan
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  • Assuming you are on the lowest possible step ($0$ or $1$?) what is the distribution of your movement? $51$% forward, $49$% stationary? Or $100$% forward? ... – jameselmore Aug 26 '15 at 20:46
  • 51% forward, and 49% backwards. You never stay stationary from one step to another.

    So you would be on the -1th step if you go below 0. It's weird, but you'd still eventually have to make it to the top.

     – Tristan Aug 26 '15 at 20:48
  • Ok, got it... so you have infinite steps, and you are beginning at $1$, but terminating at step $26$? – jameselmore Aug 26 '15 at 20:54
  • Yup! That's what I meant. Sorry for not being clear. – Tristan Aug 26 '15 at 20:55

1 Answers1

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A similar version of this question is already answered at Expected number of steps in a random walk with a boundary. I understand that here the "coin" is biased but the underlying theory is the same.

Community
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MahoganyConvergence
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