Date: Fri, 1 Jul 2005 01:29:28 +0000
Mime-Version: 1.0 (Produced by PhpWiki 1.3.11p1)
Content-Type: application/x-phpwiki;
  pagename=Gerrymander;
  flags="";
  author=chris;
  version=1;
  lastmodified=1120181368;
  author_id=chris;
  hits=368;
  charset=iso-8859-1
Content-Transfer-Encoding: binary

Q: You have two urns and 100 marbles, 50 white and 50 black.  You wish to
maximize the odds that someone picking a marble at random from one of
the urns will pick a black marble.  How do you do so, and what are the
maximum odds?


A: Put one black marble in one urn, and all the other marbles in the
other urn.  Then the person will have a 1 in 2 chance of picking the
urn with the single black marble, and a 1 in 2 chance of picking the
urn containing 49 black marbles out of 99.  This gives a combined odds
of 148 : 198 or 74 : 99 or a little under 3 : 4 of picking a black marble.

This is the principle behind gerrymandering of voting districts.