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

Home > Probability
Attributed to Lewis Carroll (Posted on 2017-11-07) Difficulty: 2 of 5
A bag contains one counter, known to be either white or black.
A white counter is put in, the bag shaken, and a counter drawn out, which proves to be white.
What is now the chance of drawing a white counter?

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution 2 scenarios: with and without replacement Comment 4 of 4 |
The following assumes it's equally likely to contain a black or a white counter before placing the new white counter.

Without replacement:

P(original was white and white was drawn) = 1/2
P(white would be drawn somehow) = 1/2 + (1/2)*(1/2) = 3/4

P(original was white given the known outcome of white) = 1/2 / (3/4) = 4/6 = 2/3

If the drawn counter is not placed back into the bag then that is the probability that the lone counter remaining in the bag is white as that would happen if and only if the original counter were white.

With replacement:

If the drawn counter were placed back in the bag then the chance of drawing another white counter is 2/3 + (1/3)*(1/2) = 2/3 + 1/6 = 5/6.

  Posted by Charlie on 2017-11-07 14:19:37
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 (4)
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