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.)
re: Without replacement (spoiler) | Comment 2 of 4 |
(In reply to Without replacement (spoiler) by Steve Herman)

What if I turn your argument around and ask what is the probability that the new counter was drawn out?  Taking a look, your argument has 2 out of 3 ways to draw the new counter so by the logic that that each scenario is equally likely then the probability is 2/3.  This is clearly false as there are exactly two counters in the bag and they are both equally likely to be drawn.


So something is wrong, specifically that each of the three scenarios have an equal chance of occurring.  There is an equal chance of drawing the original counter vs the new counter.  This then implies that scenario c) has a 1/2 chance of happening.  That leaves each of scenario a) and b) a 1/4 chance each.  Thus the probability of drawing a white counter is 3/4.

This problem is equivalent to being given a bag with two coins, one is normal heads/tails and the other is double heads.  And then being asked what is the probability that heads shows up when one coin is chosen at random and flipped.  There are three heads and one tail, so the probability is 3/4.

  Posted by Brian Smith on 2017-11-07 12:52:31
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 (13)
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