Sunday, 17 July 2011

Survivor... Black or White?

A really nice probability problem to talk with students about.  What approaches do they use? 

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?

This is another nice problem I found at Futility Closet.  Really an entertaining blog.  Greg cites this as from the 1983 Australian Mathematical Olympiad, via Ross Honsberger, From Erdös to Kiev, 1996.  Another nice problem for teachers to add to their files.

If you can't figure it out,Alexander Bogomolny has a solution for the problem at his "Cut-the-knot" web site... a great source for students (and teachers) to explore. 
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