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Three Curtain Problem


rstrats
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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 - who knows where the car is so as not to end the game prematurely -
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?

Edited by rstrats
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Chill, guys. It's a hypothetical question!!

I would have to say it depends on what was behind curtain #1. If it were something that I needed more than a new car I would keep it.



So its a hypothetical question, do you not think that we don't know that. Even being a hypothetical question, it needs a proper follow up, not for us Christains to chill out.
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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?

What would be the advantage of changing to curtain #2?
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salyan,

re: “How do you double your chances of winning by switching?”


Annie,

re: “What would be the advantage of changing to curtain #2?”



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 curtain # 2.

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.

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salyan,

re: “How do you double your chances of winning by switching?”


Annie,

re: “What would be the advantage of changing to curtain #2?”



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 curtain # 2.

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.

Interesting to think about. But wouldn't the host's action then reduce the chances to 50/50, since there are only two viable spots left, one in "A" and one in "B"? "B" no longer has a mathematical advantage over "A" after the empty space is revealed.

Similarly, the odds of my drawing a red marble out of a bag which originally contained 2 reds and 1 white, after a red marble has been removed, is not 2/3, but 1/2. Edited by Annie
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Annie,

 

re: "Similarly, the odds of my drawing a red marble out of a bag which originally contained 2 reds and 1 white, after a red marble has been removed, is not 2/3, but 1/2.

 

 

That is indeed true, but it is not similar.

 

Just FYI, rstrats, Annie has gone on to glory...

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