Travis: Segment 3
1. The slides used a symmetry argument ("relabeling") to simplify the calculation. Redo the calculation without any such relabeling. Assume that the doors have big numbers "1", "2", and "3" nailed onto them, and consider all possibilities. Do you still have to make an assumption about Monty's preferences (where the slide assumed 1/2)?
To Think About
1. Lawyers are supposed to be able to argue either side of a case. What is the best argument that you can make that switching doors can't possibly make any difference? In other words, how cleverly can you hide some wrong assumption?
Argument 1: There is always a door that does not have a car behind it, and this is true regardless of your choice of doors. So, when Monty opens a door without a car behind it, he isn't providing you any new information and the odds have stayed the same for the remaining two doors.
Argument 2: (From my friend with whom I discussed this problem during dinner recently) I get the math behind the problem and I see that you win more often if you switch, but if I were actually on a game show I can't say that I would switch. I'm a firm believer in my "gut" feeling which would be to stick with the door I choose. Lucky people should still stay with their original choice.
Counter argument to Argument 2: When you are making your first choice, just convince yourself that you are choosing a wrong door. That way when Monty shows you the other wrong door, your "gut" will tell you that you have to switch in order to win.