(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have a countably infinite set of marbles numbered; 1, 2, 3,..., n.

I also have an urn that can hold an infinite amount of marbles.

I then place marbles 1 and 2 into the urn, and remove one of them with the following probabilities:

The probability of removing a marble is proportional to its number.

So, the probability that I remove marble 1 is [tex]\stackrel{1}{3}[/tex], and that I remove marble 2 is [tex]\stackrel{2}{3}[/tex].

Once a marble is removed, I then place marbles 3 and 4 into the urn. I

Now if marble 2 was removed earlier, then marbles 1,3,4 are in the urn. The probability of removing any of them are now respectively, [tex]\stackrel{1}{8}, \stackrel{3}{8}, and \stackrel{4}{8}[/tex]

I keep adding and removing marbles as above, in order of their number.

I am asked to show, that there is a positive probability that marble 1 remains in the urn forever.

2. Relevant equations

3. The attempt at a solution

Not quite sure how to pin this down. Any help is much appreciated!

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# Homework Help: Probability: Infinite marbles placed in, and selected from an urn

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