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 2008-01-07, 17:51 #1 davar55     May 2004 New York City 2·32·5·47 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?
2008-01-07, 18:17   #2
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by davar55 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?
Oy vay. Not again.

 2008-01-07, 18:45 #3 ewmayer ∂2ω=0     Sep 2002 República de California 263768 Posts Where's Marilyn "Self-Proclaimed World's Smartest Woman" Vos Savant when you need her? For that matter, where's Monty Hall?
 2008-01-07, 20:46 #4 davar55     May 2004 New York City 2×32×5×47 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.
 2008-01-07, 20:56 #5 ewmayer ∂2ω=0     Sep 2002 República de California 263768 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. 2008-01-07, 21:00 #6 Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 100001100101002 Posts Quote:  Originally Posted by ewmayer 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.
A major US newspaper had an article on 3-wheeled motorcycles recently. It seems that in some areas, riders need not have a valid motorcycle license to ride them.

2008-01-07, 21:18   #7
davieddy

"Lucan"
Dec 2006
England

2·3·13·83 Posts

Quote:
 Originally Posted by davar55 After you make a choice, one of the other doors is opened revealing a tricycle.
Was there the chance of it revealing the car?
I am undeterred by the poohpoohing tone of the
initial response

2008-01-07, 21:37   #8
davar55

May 2004
New York City

423010 Posts

Quote:
 Originally Posted by davieddy Was there the chance of it revealing the car?
No. A tricycle was inevitable.

(I have nothing against tricycles.
They certainly are fuel-efficient and child-friendly.)

2008-01-07, 22:20   #9
davieddy

"Lucan"
Dec 2006
England

194A16 Posts

Quote:
 Originally Posted by davar55 No. A tricycle was inevitable.
Thanks. I had anticipated the follow up question where
one of the remaining doors is opened at random.

I hope no-one 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")

 2008-01-07, 22:31 #10 Brian-E     "Brian" Jul 2007 The Netherlands 2·23·71 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?
 2008-01-07, 22:41 #11 davieddy     "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 2008-01-07 at 23:08

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