A brain teasing probability puzzle
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Kaines
Potato Supreme
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Texas A&M University School of Law
It was Texas Wesleyan when I attended, then A&M bought them.
And you've been wrong the whole time. The math works better to illustrate the idea when there are an infinite number of boxes to choose from. If there are an infinite number, your first choice is wrong. Every time, it's wrong. When the host removes all but 1 other possibility, switching is a guaranteed win. Now go away.
Sabbat
Trakanon Raider
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100%
Everyone knows that a one in ten chance is 10%, but one in a million is a guarantee.
Kaines
Potato Supreme
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Let's change what's in the boxes just for illustrative purposes (it actually doesn't change the odds). I'm going to put number 1 - 20 under 20 different boxes. You're goal is to pick the box with a 20 under it. After you make your first pick, I remove 18 "wrong" choices, showing you 18 different numbers, but none of them are the number 20. Then I ask if you want to switch boxes. Do you?
Loser Araysar
Chief Russia Correspondent / Stock Pals CEO
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I think the real stumbling block is assuming that some sort of arbitrarily decided sequence of events has an effect on the final outcome.
In my example, the 1,000,000th flip is still 50/50 regardless of the fact that the previous 999,999 flips have been tails.
In my example, the 1,000,000th flip is still 50/50 regardless of the fact that the previous 999,999 flips have been tails.
Jait
Molten Core Raider
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Or they're trolling. But I'll assume they're just very Human.
They also get caught up on the idea that the box they think they have a better chance of winning by switching to now has exactly the same chance of being right as the one they originally picked. It's a new scenario, nothing that came before has any impact on the final choice except their belief that they couldn't have picked the right one from the get go. That's just faulty intuition, not logic.
They also get caught up on the idea that the box they think they have a better chance of winning by switching to now has exactly the same chance of being right as the one they originally picked. It's a new scenario, nothing that came before has any impact on the final choice except their belief that they couldn't have picked the right one from the get go. That's just faulty intuition, not logic.
Kaines
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Actually it's the knowledge that the box you initially picked has 1/n chance of being right and a (n-1)/n chance of being wrong. When given the chance to move off of my (n-1)/n chance of being wrong, you should take it, especially as n gets larger. Hence my illustration of an infinite number of boxes to choose from. Your first choice is (inf-1)/inf chance of being wrong, which is 1/1. 100% chance of being wrong. Switching IS the only logical answer.
Kaines
Potato Supreme
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Only if I got to choose a side at random and thought it was the number 100. Then you remove 98 "wrong" choices and ask me to pick AGAIN. The fact that two choices are made is the important part. You are trying to switch what's in the box by flipping the coin AFTER you removed the sides. The flip happens BEFORE you take away 98 sides and then the game begins.
Jait
Molten Core Raider
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Read the original post. We're talking about 3 choices, not 100, not infinite.
If there were more than 3, you'd be right. Because the wrong choice would stay through the elimination despite always being wrong. I should have said a 3 sided coin, that might have made it more simple for you to grasp.
edit: The odds your box is correct increased just as much as the other box. You had a 33% chance of being right the first time, so did the other box.
If there were more than 3, you'd be right. Because the wrong choice would stay through the elimination despite always being wrong. I should have said a 3 sided coin, that might have made it more simple for you to grasp.
edit: The odds your box is correct increased just as much as the other box. You had a 33% chance of being right the first time, so did the other box.
Kaines
Potato Supreme
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Wrong. The odds your box is right/wrong never changes. Because the correct box is never changed.
Loser Araysar
Chief Russia Correspondent / Stock Pals CEO
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