Problem 1:

   At the beginning of the a game an urn contains 100 white marbles and 100 black marbles.  Each turn consists of randomly taking out two marbles.  If they are both the same color, a white one is put back.  If they are different colors, a black one is put back.  Thus after each turn there is one less marble then before.

If you had to bet on which color the last marble would be, which color would you choose and what would be the probability of winning the bet?

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