You're playing a game. You start with a box with one black marble and one white marble, and you sample twice with replacement. If you select the white marble both times, you win. If you select the black marble either time, you add another black marble and try again. On each round, you sample twice with replacement, winning if you select the white marble twice, otherwise adding another black marble and moving on to the next round.

What is the probability that you eventually win? Equivalently, if P(n) is the probability that you win on or before round n, what is the limit of P(n) as n -> infinity?

(In reply to re: No Subject by Charlie)

Sorry, you're right ... I was thinking that all along as I formulated that plan, but I wrote it down wrong there. It's easier to think of the probability for losing by a certain time than winning in the same time in this problem, and you can always flip it after you take the limit, but in this case you don't need to.

Posted by Avin on 2004-11-01 15:22:52