All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Probability
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: ( Back to comment list | You must be logged in to post comments.)
re(2): No Subject | Comment 7 of 12 |
(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

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information