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Marble Game (Posted on 2004-11-01) Difficulty: 4 of 5
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?

See The Solution Submitted by Brian Smith    
Rating: 4.2000 (5 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
answerK Sengupta2007-08-23 14:47:35
MaybeMe2005-01-07 14:25:23
SolutionFancier answerFederico Kereki2004-11-01 23:22:53
Some Thoughtsre(2): Fancy Shmancy AnswerFederico Kereki2004-11-01 23:06:36
re: Fancy AnswerAvin2004-11-01 15:24:41
re(2): No SubjectAvin2004-11-01 15:22:52
SolutionFancy AnswerFederico Kereki2004-11-01 15:17:34
re: No SubjectCharlie2004-11-01 14:37:33
Some Thoughtssome valuesCharlie2004-11-01 14:25:51
re: No SubjectAvin2004-11-01 14:03:11
SolutionNo SubjectAvin2004-11-01 14:01:17
SolutionMy Solution and Spoiler Hintowl2004-11-01 13:55:46
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