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Bean coloring (Posted on 2015-07-13) Difficulty: 4 of 5
Start with a bag containing 5 white beans. Randomly draw one at a time employing the following rule:

If the bean is white, color it black and put it back in the bag;
If the bean is black, keep it out.

What is the probability that at some point there will be a single white bean in the bag?

Generalize to start with N beans.
Does the probability converge, and if so, to what value?

No Solution Yet Submitted by Jer    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(3):Correcting My previous analytical solution | Comment 8 of 11 |
(In reply to re(2):Correcting My previous analytical solution by Charlie)

Also, going back to 


P(3,3,1)=P(2,4,0)*1

this neglects the + P(2,3,2)*2/5 contribution.

Again, this is as far back as I've analyzed in your synopsis.

PS

P(4,3,0)=P(3,3,1)*1 should be P(4,3,0)=P(3,3,1)*1/4, as the other 3/4 is going to P(4,2,2) as you specify.

Edited on July 15, 2015, 9:47 pm
  Posted by Charlie on 2015-07-15 21:42:51

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