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?