Paradoxes in probability  Many of the following questions, which
are simple, have several different "reasonable" answers. 
Depending on what assumptions you make, most of the questions
have several distinct correct answers, too.  Your task is to
find answers you can defend and to identify the assumptions
needed to justify your answers.  Please be prepared to present
and justify your answers in class next week.  The Monty Hall
problem  Game show host Monty Hall ("Let's Make a Deal") asked
winning contestants to select one of three closed doors.  Behind
exactly one of the doors was a valuable prize.  Occasionally,
after the contestant had selected a door but before it had been
opened, Hall would open a different door to show it did not
contain the prize.  He then allowed the contestant to change her
choice to the remaining closed door.  Assuming Hall did not know
which door contained the prize (and therefore needed an
assistant to identify the door to open, to avoid inadvertently
revealing the prize), what is t