20080107, 17:51  #1 
May 2004
New York City
5×7×11^{2} Posts 
A Wise Choice
You're given a choice of three doors, behind each of which is a prize 
one, an expensive car, the others, worthless tricycles. The car is placed behind a random door. After you make a choice, one of the other doors is opened revealing a tricycle. You are then given the option to keep your original choice or switch to the other unopened door. Assuming you want to win the car, should you stay or switch? 
20080107, 18:17  #2  
Nov 2003
1D24_{16} Posts 
Quote:


20080107, 18:45  #3 
∂^{2}ω=0
Sep 2002
República de California
10110111001111_{2} Posts 
Where's Marilyn "SelfProclaimed World's Smartest Woman" Vos Savant when you need her?
For that matter, where's Monty Hall? 
20080107, 20:46  #4 
May 2004
New York City
5·7·11^{2} Posts 
I should have realized this has been discussed, but I think it
was quite a while ago. If it's not worth it, then ok, let it go. 
20080107, 20:56  #5 
∂^{2}ω=0
Sep 2002
República de California
3^{2}×1,303 Posts 
Anyway, what have you got against tricycles? A very underrated form of transportation, sure to come back into vogue once U.S. gas prices hit $5 per gallon later this year.

20080107, 21:00  #6 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2^{5}×7×47 Posts 
A major US newspaper had an article on 3wheeled motorcycles recently. It seems that in some areas, riders need not have a valid motorcycle license to ride them.

20080107, 21:18  #7 
"Lucan"
Dec 2006
England
2×3×13×83 Posts 

20080107, 21:37  #8 
May 2004
New York City
5·7·11^{2} Posts 

20080107, 22:20  #9 
"Lucan"
Dec 2006
England
2×3×13×83 Posts 
Thanks. I had anticipated the follow up question where
one of the remaining doors is opened at random. I hope noone posts a link to the previous discussion or anything else before appropriate thinking has taken place in this thread. (See discussion of googling puzzles in your "Count the triangles") 
20080107, 22:31  #10 
"Brian"
Jul 2007
The Netherlands
2·3·5·109 Posts 
Was it agreed before the first door was chosen that the next thing that would happen would be the opening of another door revealing a tricycle?
Or could the original choice of door have influenced what happened next? 
20080107, 22:41  #11 
"Lucan"
Dec 2006
England
2·3·13·83 Posts 
I choose door A and there are 4 outcomes: The car is in A and you open door B (1/6) The car is in A and you open door C (1/6) The car is in B and you open door C (1/3) The car is in C and you open door B (1/3) You swap. (You now know which of the two not to swap with!) In Bridge this is known as the "Principle of restricted choice". The chance of the car being behind door A remains 1/3, but that now leaves 2/3 for the car lying behing the unchosen door. Last fiddled with by davieddy on 20080107 at 23:08 
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