MATH STINGER #10

    by Dr. Joel C. Fowler
    Assistant Professor of Mathematics

    
   
     The puzzle for this issue concerns probability.  You are
given 100 marbles, 50 black and 50 white, to be distributed into
two urns in any way you wish.  Once they are distributed an urn
will be chosen at random and a marble drawn from it at random. 
How should you distribute the marbles in the urns if you wish to
make the probability of picking a white marble as large as
possible?  A second related problem is to determine how the white
balls should be distributed if the black marble distribution is
fixed with the first urn containing 20 black marbles and the
second containing 30?  A knowledge of basic calculus may be of
help in solving this second problem.
    

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