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October 29th, 2011, 03:54 PM   #1
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Difficult question!

I have been trying to work on this question but the answer keeps escaping me. I tried creating a binomial tree for various values of k but I still can't figure out the general case for this.

Two bags contain k identical balls each. A game is played where one ball is picked at random(with all
2k balls equally likely to be picked) and moved from the current bag it is in to the other bag. When one
bag is empty, the game stops. If Tk is the number of turns before the game finishes, find an expression
for E[Tk].

Any help or hints would be greatly appreciated!
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