EcoModder Forum Two cars, one goat

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 02-23-2015, 03:01 AM #1 (permalink) Not Doug     Join Date: Jun 2012 Location: Show Low, AZ Posts: 10,034 Chorizo - '00 Honda Civic HX, baby! :D 90 day: 35.35 mpg (US) Mid-Life Crisis Fighter - '99 Honda Accord LX 90 day: 32.86 mpg (US) Thanks: 6,669 Thanked 1,913 Times in 1,455 Posts Two cars, one goat My cousin posted an article about Marilyn vos Savant on Facebook. Twenty-five years ago, she "solved" the Monty Hall Problem, and ten thousand people wrote in to tell her that she was wrong. It was simply that, if presented with three doors, told that two doors each have a goat, but the third has a car, and told to choose one, what is the chance of correctly choosing the door hiding the car if you change your mind after shown the third door? The writer said that you would think that you have a fifty-fifty chance regardless, but vos Savant argued that it would be two-thirds. Many paragraphs later, I understood that, if shown the car, your chances of choosing the car increase to 100% if you chose another door, but change your mind--presumably to the open one showing the car. If you do not choose the car after seeing it, there is a 100% chance that you are an idiot. Seriously, I do not use that term lightly. There is only one car, you are shown the car, so why would you say "No thanks, the one and only car is behind another door?" So, you are correct in thinking that you have a 50-50 chance whether you change your mind or not, assuming that the third door does not have the car. http://priceonomics.com/the-time-eve...ign=pockethits
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 02-23-2015, 04:38 AM #3 (permalink) Too many cars     Join Date: Oct 2009 Location: New York State Posts: 1,354 CRXFi - '88 Honda CRX XFi Insight 256 - '00 Honda Insight Team HondaGen-1 Insights Insight 5342 - '00 Honda Insight Team HondaGen-1 Insights 90 day: 65.78 mpg (US) Thanks: 851 Thanked 623 Times in 369 Posts If I understand the problem correctly, it has to be a 50-50 chance. Three doors. Pick one. A door you didn't pick is opened, revealing a goat. Two doors remain, a car and a goat. You now get to switch or stay. How is that different than picking from two doors? Why would the original choice matter? And is a Lincoln Continental better than a goat? Edit: Nevermind, now I get it! __________________ Last edited by Gasoline Fumes; 02-24-2015 at 04:12 PM.. Reason: I got smarter thanks to RedDevil
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 02-23-2015, 04:48 AM #4 (permalink) Master EcoModder   Join Date: Aug 2010 Location: Philippines Posts: 2,173 Thanks: 1,739 Thanked 587 Times in 401 Posts Actually... the door opened by the host ALWAYS has a goat behind it. That's the game show format. The host CANNOT pick the winner for you. That's a given. In which case, you really do improve your chances by changing your mind. And statistics actually backs this up, strangely. Monty Hall problem - Wikipedia, the free encyclopedia You have a 2 in 3 chance of winning by changing your mind.
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Quote:
 Originally Posted by Gasoline Fumes Two doors remain, a car and a goat. You now get to switch or stay. How is that different than picking from two doors? Why would the original choice matter? And is a Lincoln Continental better than a goat?
Before he opens the door the chance is 66.7% that the car is behind one of the doors you did not choose.
When he opens one of those doors the chance the car is behind the other door is still 66.7 %, unless he accidentally opens the door with the car in which case you'll choose that door.

Two doors remain, the one you chose at first with a 33.3% that it has the car, and the door the host did not (could not) open.

As your door still has that same 33.3% chance of having a car behind it (the car did not move) the remaining door has that 66.7% chance.

Swap and sell the Lincoln for a herd of goats.
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It always takes longer than you expect, even when you take into account Hofstadter's Law.

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Last edited by RedDevil; 02-23-2015 at 05:05 AM..

 02-23-2015, 07:13 AM #6 (permalink) Not Doug     Join Date: Jun 2012 Location: Show Low, AZ Posts: 10,034 Chorizo - '00 Honda Civic HX, baby! :D 90 day: 35.35 mpg (US) Mid-Life Crisis Fighter - '99 Honda Accord LX 90 day: 32.86 mpg (US) Thanks: 6,669 Thanked 1,913 Times in 1,455 Posts That table shows all six possible outcomes, which are very limited, but the only way to have a 2/3s chance is if there is a possibility for the host to show you the car, and for you to choose that door once you know, but why would they ever do that? Are all of their contestants drunks? That would make it interesting...
 02-23-2015, 08:44 AM #7 (permalink) In the fasting lane     Join Date: Dec 2012 Location: Nieuwegein, the Netherlands Posts: 3,781 Red Devil - '11 Honda Insight Elegance Team Honda 90 day: 53.55 mpg (US) It - '09 Hyundai I10 Active Cool Team Hyundai 90 day: 29.76 mpg (US) Thanks: 1,548 Thanked 2,086 Times in 1,341 Posts You are one of many who don't get it. Don't take it personal - many smart people don't get it. Maybe you just don't want to believe there can be a 2/3 chance. Something makes you read, yet refute, the truth. You throw in an assumption "the only way to have a 2/3s chance is if there is a possibility for the host to show you the car"... What is that based on? The point is that the host shows you where the car is not, while he knows where it is. His choice of which door to open is NOT random. That changes the odds. If you choose A and the car is behind B he'll show C. Swap and you get a car. If you choose A and the car is behind C he'll show B. Swap and you get a car. Only if the car is behind door A (1/3 chance) can he choose which one to open as none has a car. If you swap you don't get the car. __________________ 2011 Honda Insight + HID, LEDs, tiny PV panel, extra brake pad return springs, neutral wheel alignment, 44/42 PSI (air), PHEV light (inop), tightened wheel nut. lifetime FE over 0.17 Gmeter or 0.1 Mmile. It always takes longer than you expect, even when you take into account Hofstadter's Law. When I drive a car I'm a driver. When I'm sitting on my couch I'm a biker.
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Quote:

The aticle was in New York Times in 1991:

Behind Monty Hall's Doors: Puzzle, Debate and Answer?
By JOHN TIERNEY,
Published: July 21, 1991

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Step one- you pick a door, whichever one you pick is meaningless.
Step two- the host shows you one door that doesn't have the prize.
Step three- you decide which of the two doors the host didn't open has the prize.

Call it "switching" or just flip a coin at that moment, it's 50/50. Your initial "choice" just narrows down the host's choice of doors, and the host's choice is the only piece of information you have.
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 Originally Posted by sheepdog44 Transmission type Efficiency Manual neutral engine off.100% @∞MPG <----- Fun Fact. Manual 1:1 gear ratio .......98% CVT belt ............................88% Automatic .........................86%