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In Reply to: No I'm not! posted by Don T on October 25, 2006 at 17:42:23:
The problem is your proof 3a."The winning door will be the selected door 1/3 of the time. So there is only a 2/3 chance that the winning door is behind the two non-selected doors."
Absolutely correct.
"In the random selection the odds are 1/2 that the winning door is revealed so the odds of randomly selecting the winning door is 1/2 * 1/3 = 1/6"
Sorry you are off by a factor of 2.
Probability calculations are really just counting.
There are 2 different doors that your 1/6 probability applies to. You need to count both possibilities.
The situation is very clean.
If random selection is made, the odds are 1/3 that you've picked the right door, 1/3 that the prize will be revealed in the 2nd round, and 1/3 that you will pass the 2nd round and it will be in the other door than which you have selected.
I did not want to do this but here is the complete list of possible outcomes:
Given doors X, Y, Z- you pick X
1. prize behind X- Monty reveals Y- you win by sticking
2. prize behind X- Monty reveals Z- you win by sticking
3. prize behind Y- Monty reveals Y- game ends you lose
4. prize behind Y- Monty reveals Z- you win by switching
5. prize behind Z- Monty reveals Y- you win by switching
6. prize behind Z- Monty reveals Z- game ends you loseThis is the complete set and they are equally likely given a random pick. If you count them up you will see the odds are as I have said above.
There is a similar but different count if Monty specifically chooses to reveal the losing door. Then, as you know, the 1 of 3 cases where you lose in the 2nd round become 1 of 3 cases where you also win by switching, giving 2/3 in this category.
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Follow Ups
- you are close but not correct - tunenut 19:29:36 10/25/06 (15)
- That's not the right way to count! - Don T 21:17:10 10/25/06 (14)
- I guess I will have to quit - tunenut 21:27:20 10/25/06 (13)
- Re: I guess I will have to quit - Don T 00:20:28 10/26/06 (12)
- Re: I guess I will have to quit - tunenut 07:19:05 10/26/06 (11)
- Re: I guess I will have to quit - Don T 11:56:28 10/26/06 (2)
- Re: I guess I will have to quit - tunenut 18:20:39 10/26/06 (1)
- Re: I guess I will have to quit - Don T 23:12:00 10/26/06 (0)
- Re: I guess I will have to quit - Don T 08:25:01 10/26/06 (7)
- here is your logical fallacy - tunenut 10:07:27 10/26/06 (6)
- It's still wrong. - Don T 11:41:47 10/26/06 (5)
- Please answer my three questions (NT) - tunenut 11:44:56 10/26/06 (4)
- Re: Please answer my three questions (NT) - Don T 12:04:12 10/26/06 (3)
- Re: Please answer my three questions (NT) - tunenut 12:45:51 10/26/06 (2)