When you make your first initial choice, you chances of winning are 1/3
assuming you get whatever is behind the first door you choose.
When the host exposes that a goat is behind one of the doors you didn't
pick, he just makes it so that if you picked again (from either of the
remaining doors), your chance of winning would be 1/2.
In a sense, not choosing to switch doors is also picking one of the
remaining doors, so it shouldn't matter if you switch or not, each
remaining door will have a 50% chance of being the once with the car.
Perhaps there's some small thing I'm overlooking, but I'm fairly
confident that if the host is totally neutral, and he always asks you
the question, then it won't matter if you stay or switch from the
mathematical standpoint. However, if the host wants ratings, or to deny
you the car, or whatever, then you have to take all that into account.
-- Mike
Back to the Chatroom Homepage...
Back to the Stats 154A Homepage...
This archive was generated by hypermail 1.02.