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 Fancy Answer by Federico Kereki)

Your P(n) function is incorrect - the odds of winning the second time are not just 1/3², it's (1-1/2²)* 1/3². Similarly, the odds of winning the third time is (1-1/2²)* (1-1/3²)*1/4².

Posted by Avin on 2004-11-01 15:24:41