The Last Ball

An urn contains 75 white balls and 150 black ones. A pile of black ones is also available.

The following two-step operation occurs repeatedly. First we withdraw two balls at random from the urn, then:

  • If both are black, we put one of them back in the urn and throw the other away.
  • If one is black and the other white, we put the white one back and throw the black one away.
  • If both are white, we throw both away and put a black ball from the pile into the urn.

Because the urn loses a ball at each step, eventually it will contain a single ball. What color is that ball?

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