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PUZZLE #2: THE MONTY HALL PROBLEM

This problem is famous for the controversy that has sprung up regarding
its solution; it seems to be very counter-intuitive to many people. (See
here for
more discussion.)
The problem has its source in an old TV game show, called "Let's Make
a Deal," hosted by Monty Hall. Mr. Hall (MH) goes into the audience and
picks a player (P), and this is how the game goes:

(1) MH asks P to pick a door from a row of three that are on the stage.
Behind one of the doors is a prize; behind each of the other two, a brick.
P obligingly picks a door (say door 1).

(2) MH now opens one of the doors not picked by P (say door 3)
and purposely reveals a brick.

(3) Finally MH gives P the opportunity to switch the original pick to
the other door (which is now door 2). Before the right door is
opened, P must choose either to stick with the original pick or
to switch. (The crowd goes wild giving advice at this point.)

The problem is to decide which, if either, strategy is most
likely to get P the prize.

(solution)