A brain teasing probability puzzle

Arbitrary_sl said:

Alright, how do I model the game show producer knowing this and rigging the results so that switching is always a loss?

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You let Host discard the the right choice without revealing it. So ether both choices are wrong because Host discarded the right choice. Are the right choice is only the Contestants choice because they guessed right on there initial guess. Before the Host could discard it..

Tuco_sl said:

Izo if you make a poll in the suggestions forum asking Araysar to be unbanned and it favors unbanning him after an hour I will unban Araysar

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http://www.rerolled.org/showthread.p...e-Araysar-Poll
Man or mouse, Tubro?

Siddar_sl said:

You let Host discard the the right choice without revealing it. So ether both choices are wrong because Host discarded the right choice. Are the right choice is only the Contestants choice because they guessed right on there initial guess. Before the Host could discard it..

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I don't really know what I'm doing here.

For people who aren't insane, I confirmed that if the host reveals a chest at random, the odds go back to 50/50 even when its a goat that's revealed, leaving the total odds 1/3 considering two of the six possible outcomes involve the host revealing the car. All odds go out the window if the host has a choice in which one he reveals because it then becomes a mind game

If the host picks at random it would be pretty dumb because you could just win on the host's choice.

Have you bothered watching the video, reading any explanations, or taking a stats class? It appears you have no idea what you're talking about.

I don't think anyone has taken into consideration that the box is red though.

Yeah if the host reveals a car you've already lost. If the host reveals a goat you still improve your odds by switching, it doesn't matter if he knew or not.

Come on, people...

If you stick with your box, you have a 1 in 3 chance of winning. You win if and only if you picked the $100k box at the beginning.

If you switch, you lose if and only if you picked the $100k box at the beginning. Since this has a 1 in 3 chance of being true, the probability of winning is (1 - 1/3) = 2/3. So by switching, you have a 2 in 3 chance of winning.


If the host picked one of the other chests at random, then either he reveals the $1 prize, in which case the setup is the same as above and you should switch; or he picks the $100k prize in which case it doesn't matter what you do as you have already lost.

By the way: statisticians do not generally have better intuitions about this kind of stuff. They obviously have the tools to solve this (as does everyone who has taken probability in high school -- it doesn't require any advanced techniques), but it's one of the areas where people just cannot get an intuition for. Another example of that sort is exponential growth...

If you take a sheet of paper and fold it in half 100 times (assume you can do this), how thick would the paper be?

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Do not use a calculator but try and ballpark it.

Then there's this example, which is tremendously popular in my field:

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Which is more probable?

1. Linda is a bank teller.
2. Linda is a bank teller and is active in the feminist movement.

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Statisticians get this one wrong all the time.

Soriak_sl said:

but it's one of the areas where people just cannot get an intuition for.
...
Statisticians get this one wrong all the time.

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My brother uses questions like those to "gotcha" people in job interviews. I think it is a pretty shitty way to interview people, because as you said, it just isn't intuitive and even very very smart people in the field mess shit up like that. It turns into more of a test of if the person had heard a test like that before.

Despite mathematical proofs, a wikipedia page dedicated to the problem, countless people offering expanded logic, he is still fighting the good fight. Listen man, I know you don't want to admit you're wrong.. but a lot f people smarter than anyone on this forum figured this shit long ago.

khalid_sl said:

My brother uses questions like those to "gotcha" people in job interviews. I think it is a pretty shitty way to interview people, because as you said, it just isn't intuitive and even very very smart people in the field mess shit up like that. It turns into more of a test of if the person had heard a test like that before.

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There's a set of three questions along those lines called the Cognitive Reflection Test. Someone's score on this test, it turns out, is a good predictor of anything from educational achievement to adequacy of retirement savings to general health. I actually wouldn't be opposed to using that as part of an interview...

It doesn't test how smart someone is, but it tests whether they stop and think carefully about the problem or just blurt out the first answer that comes to mind.

I'm just worried about whether or not the boxes are made out of ash. I wouldn't be allowed to transport that in my state.