monty hall problem  aha:!

another well known problem in probability is the monty hall problem.

you are presented with three doors (door 1, door 2, door 3). one door has a million dollars behind it. the other two have goats behind them. you do not know ahead of time what is behind any of the doors.

monty asks you to choose a door. you pick one of the doors and announce it. monty then counters by showing you one of the doors with a goat behind it and asks you if you would like to keep the door you chose, or switch to the other unknown door.

should you switch? if so, why? what is the probability if you don't switch? what is the probability if you do.

lots of people have heard this problem.. so just knowing what to do isn't sufficient. its the explanation that counts!