Problem
of the
Week

PROBLEM 250

You are given a bag containing ten white marbles.  You draw one out and replace it with a black marble.  You then repeat the process, replacing each white marble drawn with a black marble; each time you draw out a black marble, however, you return it to the bag.  What is the fewest number of drawings that would give you at least a 50% chance of having an equal number of black and white marbles?

(If you don't mind losing your marbles:  Same question, but suppose the bag started out with n marbles.)

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ã2006 Alberto L. Delgado