0
$\begingroup$

We start with $a + b$ balls in the urn: $a$ white and $b$ black ones.At each step we randomly choose a ball and if it's white then $m$ of the black balls in the urn turn white, symetrically for choosing black one. We put the chosen ball back in the urn. So if we've chosen white we move from $(a,b)$ state into $(a+m, b-m)$. What is the probability that at $k$ step we will choose a white ball?

So my understanding is that this is a kind of random walk on 1D with state $l$ representing the urn of $(a + lm, b-lm)$ and reachable only from states $\{l-1, l+1\}$ but the probability of the move is state-dependent and I've got stuck here.

  • 0
    Not sure the rules are clear. What happens if $b-m<0$? Do you just change all the remaining black balls white? (in which case, I suppose the game just stops...). If so, then I assume the game ends monochromatically pretty quickly. Nothing wrong with that, just trying to clarify. – 2017-02-21
  • 0
    yes if $b < m$ then we change the remaining black balls white and stay in this state forever – 2017-02-21

0 Answers 0