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

Home > Probability
The First Repeat (Posted on 2016-07-18) Difficulty: 3 of 5
A bag has 5 tokens numbered 1 to 5. Tokens are drawn with replacement until a token is repeated. What is the probability that the repeated token is the first token drawn?

What is the formula for N tokens?

No Solution Yet Submitted by Brian Smith    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re: answers | Comment 3 of 5 |
(In reply to answers by Ady TZIDON)

The difference between this problem and yours is that in this case, internal matches can halt the game prematurely.


Take for example n=2. The probability of matching the first draw is already 50% at the second draw. There's a 50% chance it did not match the first, and then the third draw terminates the game: either it matches the first or the second draw.  So there's 50% probability of a 2-draw game, with a successful match of draw 1; a 25% probability of a successful match of draw 1 on draw 3; and a 25% probability of a non-match of draw 1, as the third draw matches draw 2. The probability is 3/4, not 1/2.



  Posted by Charlie on 2016-07-18 15:13:55
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 (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information