Suppose you were a contestant on
      "Let's Make a deal the old television
      show.  The host, Monty Hall, Presents three
      doors.  One hides a luxury car; the others
      conceal scrawny goats.  YOU Must choose
        The odds Of winning the car are, of
      course, one Out of three, so without much
      thought, you pick any door.  But then
      Monty mischievously opens one of the
      other doors, revealing a goat.  Are the odd
      better if you switch your choice to the
      other closed door or if YOU stay with your
      original selection?  It seems that it doesn't
      matter.  After all, there are two doors left,
      so the chance of your being right is one out of two.

       But actually, if You switch doors, you
      are twice as likely to win.  This bizarre re-
      sult led to such controversy - even a mis-
      taken objection by the great mathemati-
      cian Paul Erdos - that it became a front-
      page article by John Tierney in The New
      York Times in 1991.
      Here's the explanation.  Of Course a goat
      was always behind one of the two uncho-
      sen doors; Monty's act doesn't reveal any
      new information.  So the initial odds of one
      out of three remain unchanged.  But now
      for the weird twist.  There must be a car
      behind one of the two closed doors; if the
      car isn't behind one door, it's behind the
      other.  So if one out of every three times
      the car is behind the door you've chosen,
      the other two times it will be behind the
      other door.  This means that the odds of
      finding the car behind that other door are
      two out of three.  As the audience might
      have correctly screamed: "Switch!