TirithRR the Mundane wrote:
AshOnMyTomatoes, Guardian of the Glade wrote:
I don't care what fancy math you want to apply to it. It doesn't matter whether you switch doors or not, that '2/3rds' odds of you having chosen the incorrect door does not apply to the new situation.
No, 2/3rds is the correct answer. Take the graphical example of all possibilities, part of which was shown in an earlier post. 2/3rds of those possibilities ends with you winning a car.
You choose Door Number 1.
[o] [x] [x] You change, you lose. Total So Far: 0/1
[x] [o] [x] You change, you win. Total So Far: 1/2
[x] [x] [o] You change, you win. Total So Far: 2/3
You choose Door Number 2.
[o] [x] [x] You Change, you win. Total So Far: 3/4
[x] [o] [x] You Change, you lose. Total So Far: 3/5
[x] [x] [o] You Change, you win. Total So Far: 4/6
You choose Door Number 3.
[o] [x] [x] You Change, you win. Total So Far: 5/7
[x] [o] [x] You Change, you win. Total So Far: 6/8
[x] [x] [o] You Change, you lose. Total So Far: 6/9
As you can see, out of all the possible outcomes when you change your door, you end up with 6 winning outcomes out of 9 total.
6 chances of winning outta 9 is a 2/3rds possibility of winning if you change your mind.
Ok I think I found the problem with your model. It doesn't take into account the fact that the opened door was definitely a loser. AND the fact that the host CAN'T open a door that is a winner, or the door you chose initially.
Lets see: (we'll have a door that the host can't open represented in bold.)
You choose door 1:
[o] [x] [x] Door 3 is opened. You change, you lose.
Door 2 is opened. You change, you lose.
[x] [o] [x] Door 3 is opened. You change, you win.
[x] [x]
[o] Door 2 is opened. You change, you win.
You choose door 2:
[o] [x] [x] Door 3 is opened. You change, you win.
[x]
[o] [x] Door 1 is opened. You change, you lose.
Door 3 is opened. You change, you lose.
[x]
[x] [o] Door 1 is opened. You change, you win.
You choose door 3:
[o] [x]
[x] Door 2 is opened. You change, you win.
[x]
[o]
[x] Door 1 is opened. You change, you win.
[x] [x]
[o] Door 1 is opened. You change, you lose.
Door 2 is opened. You change, you lose.
Your chart leaves out a few possible scenarios.