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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(2):Correcting My previous analytical solution | Comment 7 of 11 |
(In reply to re:Correcting My previous analytical solution by Dan Rosen)

I haven't checked all your equations, but this one immediately stands out:


 P(2,3,2)=P(1,4,1)*1/5
 P(2,4,0)=P(1,4,1)*1/5


Actually P(2,,3,2)  should be P(1,4,1) * 4/5.

These are basically the equivalents (when corrected) of my step-by-step calculations that come up with 0.3055388888888888888 .

  Posted by Charlie on 2015-07-15 16:39:37
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