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rstrats
Nov 13th 2010, 02:56 PM
You are a contestant on a game show. There are three curtains. Behind one of the curtains is a new car. You are asked to choose one of the curtains. Lets say that you choose curtain #1. The host of the show opens curtain #3 and there is no car behind it. The host now gives you a choice. You can stay with curtain #1 or you can change your choice to curtain #2. The question now is: would it be to your advantage to stay with curtain #1, or would it be to your advantage to change to curtain #2 or would there be no advantage either way?

Doge
Nov 13th 2010, 03:21 PM
No advantage ..just the odds drop to 50/50.

rstrats
Nov 13th 2010, 07:31 PM
Doge,

re: “No advantage ..just the odds drop to 50/50.”


Ahhhhh grasshopper, you couldn’t be more wrong. You would improve your chances to 2/3rds by switching to #2.

Doge
Nov 13th 2010, 08:31 PM
erm .. not really you just have one choice .. you can switch that round all you like.

rstrats
Nov 13th 2010, 08:41 PM
Doge,

re: “erm .. not really you just have one choice .. you can switch that round all you like.”


I’m afraid I don’t know what you mean. I wonder if you might elaborate?

Doge
Nov 13th 2010, 09:03 PM
well you pick 1 .. he takes out 3 leaving you with 1 and 2 .. and asking you to switch if you like.. this looks like he is giving you a second choice but not so .. because 1 your choice is still in the game.. had he taken out 1 and asked you to pick from 2 and 3 then you'd end up having 2 out of 3.. but as it stands you havent made a choice yet because curtain 1 is still down. He may as well have started from 10 down to 2 you'd still end up 50/50.

rstrats
Nov 13th 2010, 09:29 PM
Doge,

I still don’t understand what you are saying. At any rate, you have a 2/3rds chance of getting the car if you switch to curtain #2.

rstrats
Dec 9th 2010, 12:07 AM
Doge, look at it this way: What if after your initial pick of curtain #1, I told you that you could stay with #1 or switch to BOTH #2 and #3? My guess is that you would switch so that you could look behind both curtains in spite of the fact that you KNOW that at least one of the curtains does not have a car behind it. Lets say that the first curtain that you open is #3 and you find that there is no car behind it. You now get to open curtain # 2, giving you 2 chances. What is the difference if you open curtain #3 or the host opens curtain #3 for you? Either way, you get to look behind both curtains.

You can also think of it as two areas. Area “A” contains curtain #1 and area “B” contains curtains #2 and #3. There is a 1/3rd chance that the car is in area “A” and a 2/3rds chance that it is in area “B”. Before opening any curtains, you KNOW that at least one of the curtains in area “B” doesn’t have the car behind it. So by opening a curtain in area “B” that doesn’t have a car behind it doesn’t change the 2/3rds odds that area “B” still has a car in it.

awestruckchild
May 17th 2011, 07:21 AM
I don't need a car.....but I sure could use those curtains!

rstrats
Jan 8th 2012, 12:52 PM
I need to add that the host knows where the car is so that he doesn't end the game prematurely.

otis lilly
Jan 8th 2012, 03:18 PM
Doge,

re: “No advantage ..just the odds drop to 50/50.”


Ahhhhh grasshopper, you couldn’t be more wrong. You would improve your chances to 2/3rds by switching to #2.

no matter which of the last 2 he chooses it is still the same statistal chance
it is not improved one bit by switching the choice
he had a 33.3333333% chance if being right then there was 3 choices.
but when 1/3 of them was removed there are now only 2 choices the statistics start over for beginning of new choice.
which is 50 % 50/50
and mathmatically his chances between the first choice he made, and the second chance he is about to, has only changed from: 33% to 50% a change of 17%
1 in 2 chances are still logically way way better lol
but changing the choice on 1 of 2 is no better chance than sticking with 1 of 2


I have a air compressor that weighs 203 pounds if i start it up untill it says it has 125 lbs of air in it. how much does it weigh if i move it?

Indueseason
Jan 8th 2012, 05:34 PM
I don't need a car.....but I sure could use those curtains!

:rofl::rofl:

Still wiping tears from my eyes after reading this!:lol:

As for the question, best move to curtain 2. Number 1 has the original 1/3 chance of being the car, whereas curtain 2, now curtain 3 is opened, has a 2/3 chance of being the car. Look up Monty Hall problem for details.

blessings to you :hug:

Standing
Mar 24th 2012, 04:19 AM
You still have a 1 in x chance either way. The difference now is you know that 3 is not it. So the factor that is changing is the x not the 1. You still have a 1 in x chance. It doesn't increase to a 2 in x chance.

ImpatientlyWaiting
Jun 24th 2013, 12:33 AM
rstrats has the right of it. This is an old puzzle/game/mathematical problem that has been kicked around for a very long time. It is best to switch.

rstrats
Oct 6th 2013, 03:39 PM
Standing,

re: "You still have a 1 in x chance either way. "

If after your pick of curtain #1 and before any curtain was opened, the host told you that you could switch to both curtains 2 and 3, what would you do?

rstrats
Feb 21st 2016, 01:08 PM
ImpatientlyWaiting,
re: "It is best to switch."

Anyone disagree?

pekoe
Mar 15th 2016, 05:00 PM
I don't need a car.....but I sure could use those curtains!
But if you won the car, you could sell it and buy curtains....along with
furniture to match.

Geoff Primanti
Apr 17th 2016, 12:57 AM
You start out with a 1 in 3 chance and pick curtain #1. After curtain #3 is taken away there is still a 1 in three chance in all, but curtain 3 is gone so you have to pick between 1 and 2. You picked 1 at first and if it is 1 then your first pick at 1 in 3 odd was correct. Now that curtain 3 is gone if you change to curtain 2 you lose the game. All in all it was 1 in three and that doesn't change. Now that curtain 3 is gone if you switch to curtain 2 you have just taken a new chance based on what seems to be 50-50 odds but in fact it has always been 1 in 3.
If I started with 1 and it was actually 2 then changing to 2 would win the game but only because the car was behind #2 in the first place. If I had picked #2 in the beginning then switching to #1 would lose the game and staying with #2 would win it.

The fact of the matter is that the odds are set in stone because picking a different curtain doesn't change the location of the car. After #3 is gone you now have a 50-50 chance of picking the right one whether you stay with the one you have or switch.
Personally I would stick with my first pick because I would figure that the game show host is trying to influence my decision to something different by giving me a chance to pick something different.

If I knew that the game show had at its motive for the contestant to win more often than not then I might change my pick, figuring that the game show host wants me to win and that is the reason fot the second chance. But you know they're in it for the money and don't want to lose that car (although their commercial sponsors would certainly pay for it).