Three Curtains

[rstrats]

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]

Re: Three Curtains

No advantage ..just the odds drop to 50/50.

[rstrats]

Re: Three Curtains

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]

Re: Three Curtains

erm .. not really you just have one choice .. you can switch that round all you like.

[rstrats]

Re: Three Curtains

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]

Re: Three Curtains

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]

Re: Three Curtains

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]

Re: Three Curtains

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]

Re: Three Curtains

I don't need a car.....but I sure could use those curtains!

[rstrats]

Re: Three Curtains

I need to add that the host knows where the car is so that he doesn't end the game prematurely.

[otis lilly]

Re: Three Curtains

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]

Re: Three Curtains

I don't need a car.....but I sure could use those curtains!

Still wiping tears from my eyes after reading this!

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

[Standing]

Re: Three Curtains

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]

Re: Three Curtains

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]

Re: Three Curtains

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?