A brain teasing probability puzzle

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Hoss

Hoss

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Zuuljin_sl said:
It was so obvious to me that the answer is 1), but knowing it was a trick question, I had to google it to see what the 'gotcha' was, since I had to be wrong to answer it so fast.... Only to find that the answer is 1). I really don't know anyone could possibly answer 2). Something more general is always more probable than something specific. How is that not extreme common sense?
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I was stuck on, "How the fuck do you know she's a teller?" and moved on

Voyce_sl said:
2. Monty Hall has a 2/3 chance of being left with the car, after the contestant chooses.
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You could also say monty has a 100% chance of having a goat. Which is handy, because he's going to throw a goat out when he resets the game in the second round.

What happens if we set it up like I said earlier, and your initial choice is what snack do you want from the candy machine? So monty throws away one box, and obviously of the 2 boxes left (according to prevailing "logic" around here), one would have a 33% chance of being the prize, and the other a 66% chance. So which box is which? Or are you arguing that the act of choosing is somehow altering what's inside the boxes?

What if there are 2 contestants, and at the end of the first round, the unpicked box is revealed to be a goat? Do they both have a 66% of winning if they switch?

Zuuljin_sl said:
As to Araysar, I don't think his problem is with the math per se. His issue is he doesn't understand that the first choice matters. He see's that under all cases, the host throws away an option, so he thinks you can safely just ignore his action. Ignoring him since 100% of the time he picks a goat, your really only left with 2 choices: Your door has a car and the other door has a goat, or your door has a goat and the other door has a car. Hence 50/50.
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To be more precise, in all cases, the host will throw away a losing option. I asked earlier if anyone had ever compiled the actual results from the show, and I don't see where anyone was able to find them. But, I've been thinking about it and I'm not sure the game was played like this on the real show, so while interesting, those results would probably be irrelevant.

I always wondered if anyone ever took their goats home. I mean, a goat aint a bad prize unless you live in the city.
 
N

Northerner

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In the actual show, the host could choose to show a goat or not. Given that he had knowledge of the contents of all the boxes **and was not forced to show a box**, this could be informative or misleading as desired.

The Monty Haul scenario however is not that situation. It is clear and given the rules of the problem, the statistics are equally as clear. Conflating the two is misleading.
 
Z

Zuuljin

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Hoss_sl said:
You could also say monty has a 100% chance of having a goat. Which is handy, because he's going to throw a goat out when he resets the game in the second round.

What happens if we set it up like I said earlier, and your initial choice is what snack do you want from the candy machine? So monty throws away one box, and obviously of the 2 boxes left (according to prevailing "logic" around here), one would have a 33% chance of being the prize, and the other a 66% chance. So which box is which? Or are you arguing that the act of choosing is somehow altering what's inside the boxes?

What if there are 2 contestants, and at the end of the first round, the unpicked box is revealed to be a goat? Do they both have a 66% of winning if they switch?

To be more precise, in all cases, the host will throw away a losing option. I asked earlier if anyone had ever compiled the actual results from the show, and I don't see where anyone was able to find them.
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1. Host doesn't 'reset' the game. That's the point.
2. If you don't get to pick, your chance is 50/50. Choosing does not alter whats inside the box, it alters the probability of whats inside the box.
3. I'm assuming you mean 2 contestants and the host. They are 50/50 and switching does nothing.
4. There was a simulator posted earlier that does exactly what the stated problem says. And the results were 33/66.

I'm done explaining it, but I'll answer any questions since that seems a bit more constructive.
 
ziggyholiday

ziggyholiday

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Tea_sl said:
The chance of picking the car is 1/3.
The host eliminates a goat.
You don't switch.
The chance that you picked the car remains the same - 1/3.

It's not an independent event. The way you're looking at it the doors are randomized again.
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This should have ended it for everyone.
 
Hoss

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Zuuljin_sl said:
1. Host doesn't 'reset' the game. That's the point.
2. If you don't get to pick, your chance is 50/50. Choosing does not alter whats inside the box, it alters the probability of whats inside the box.
3. I'm assuming you mean 2 contestants and the host. They are 50/50 and switching does nothing.
4. There was a simulator posted earlier that does exactly what the stated problem says. And the results were 33/66.

I'm done explaining it, but I'll answer any questions since that seems a bit more constructive.
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It alters the probability? How can the act of selecting alter anything real about the object?

#3 flies in the face of what you guys are trying to say. How can it be 50/50? The choices in the second round were "informed" exactly the same as the second round in the traditional monty hall problem. Would it help if the contestants didn't know about each other?

Which simulator? The only one I looked at was flawed because it ran through what it thought were the 3 possible scenarios, ignoring the 4th (you pick the car in the first round and the host exposes the other goat). If there's one that truly picks randomly, link it again please.

No need to explain it again, I understand the math perfectly. It's a neat trick, but nothing more. Before you appeal to authority again, realize that they're not exactly launching rockets with the monty hall math. Nothing short of real live data (or experimenting, since the real TV show didn't do it this way) would convince me it's not a trick.
 
T

The Master

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The only linked simulator covers all three scenarios and there are only three. If you pick the car, switching loses. If you pickedeithergoat, switching wins. This really is not at all complicated.

If you want "real data" you can go pirate the Mythbusters episode. They did the stupidly simple test of actually doing it, 100 times for each of the two guys. One always switched, one never switched. Results? Guy who always switched won ~66% of the time, guy who always stayed won ~33% of the time. Which, if it were actually a 50/50 chance, is so unlikely that you'd need to actually understand statistics for me to explain how unlikely it is.
 
Z

Zuuljin

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Hoss_sl said:
It alters the probability? How can the act of selecting alter anything real about the object?

#3 flies in the face of what you guys are trying to say. How can it be 50/50? The choices in the second round were "informed" exactly the same as the second round in the traditional monty hall problem. Would it help if the contestants didn't know about each other?

Which simulator? The only one I looked at was flawed because it ran through what it thought were the 3 possible scenarios, ignoring the 4th (you pick the car in the first round and the host exposes the other goat). If there's one that truly picks randomly, link it again please.
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1. Selecting, and then the hosts action gives you more information. More information changes the probability. If you chose door 1, and the next round the host truthfully told you the car was behind door 2, then there is 100% chance the car is behind door 2. Or if he told you that the car is behind your door, then your original choice now has 100% chance to be a car. So, more information changes the probability.
2. Because if there are 2 people, that means the host can only open 1 door, and since the host can only show a goat, that means the car has to be behind either the first or second contestants door. That scenario doesn't really make sense though because if the host can only open a goat, but the 2 contestants already chose the goats, what does the host do?
3. The probability is based off the car. The order of the goats doesn't matter. Think of it as either winning(W) or losing(L). So you have W-L-L, L-W-L, or L-L-W. That's 3 choices.
4. It is a trick. One that your falling for.
 
Hoss

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The Master_sl said:
The only linked simulator covers all three scenarios and there are only three. If you want "real data" you can go pirate the Mythbusters episode.
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So none of them actually picked randomly? That's what I suspected, they're invalid. Yeah, I'd kinda like to see what the mythbusters did with it, I wasn't able to find it.

Zuuljin_sl said:
2. Because if there are 2 people, that means the host can only open 1 door, and since the host can only show a goat, that means the car has to be behind either the first or second contestants door. That scenario doesn't really make sense though because if the host can only open a goat, but the 2 contestants already chose the goats, what does the host do?

4. It is a trick. One that your falling for.
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2. The contestants will only pick 2 goats 1/3 of the time. All the rest of the times though, according to the theory, they'd both have a 66% chance of winning if they switched. This is supposed to be a gameshow where the events only happen once, so assume it just happens that this time, one of the contestants picked right in the first round and there is a goat for monty to show and discard. Do they both have a 66% chance of winning if they switch?

4. In theory, there is no difference between theory and practice. In practice, there is. If you haven't seen real world evidence of it, then it might be you who's falling for something, my friend.
 
Mist

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What if this gameshow is set on an airplane, and that airplane is on a giant treadmill? Can the show take off?

What if it's underwater and there's ancient aliens at the bottom of the ocean, and the goat is now a sharknado?
 
S

Soysauceonrice_sl

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Hoss_sl said:
So none of them actually picked randomly? That's what I suspected, they're invalid. Yeah, I'd kinda like to see what the mythbusters did with it, I wasn't able to find it.
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The mythbusters clip isn't on youtube, but they tested two parts of the myth.

1. People have a STRONG tendency to stay, because their intuition tells them the probability is 50/50, and they see the switch as a ruse: Confirmed, everyone tested decided to stick.

2. They played 100 games to test the theory that switching is always better. This was also confirmed.

If you want to just see someone play the game out, there's plenty of clips for that. I saw this problem worked out in this bbc documentary a few years back, for example.



Edit* I found the episode.

http://www.watch-tvseries.net/series...of-Mythfortune

The first half is tested first, the second half is tested at around 13 minutes in.
 
drmandolin

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I am fairly certain Captain Kirk would agree with Araysar, even if it was just to piss off all of you Vulcans and your damned pointy-ear'd logic.
 
iannis

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Soysauceonrice_sl said:
The first half is tested first, the second half is tested at around 13 minutes in.
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I basically hate mythbusters for the gay format of their show. Every once in a while they'll have an interesting myth that they "bust". As in find an excuse to blow something up. But they always do 2 or 3 per show, and they always break them into 5 minute segments.

I mean fuck those hipster jackoffs. We're about to blow something up! followed by 10 minutes of watching the asian dude build a robot and talking about how cool it's gonna be to smash something with it.

Fuck that show.
 
Dyvim

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Daelos_sl said:
What if I want a goat.
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Then wait for the revealed goat, board your starship, make a slingshot run with warp 10+ back at the sun and travel back in time. Beam back down and tell yourself which door contained the goat and kaching 100% win on your side.
But beware to not touch yourself or the whole space time continuum may collapse.
 
Szlia

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Adebisi_sl said:
Can someone please explain the problem to me for the 17th time. This time in musical form.
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*cough*cough*

Here is a problem about goats and car (chorus: goats and car!)
That confuses our good friend Araysar (chorus: Araysar!)
Here is a problem of doors and choices (chorus: doors and choices!)
In musical form, 'Bisi rejoices (chorus: he rejoices!)

There are three closed doors and one you must choose
A car and two goats are hidden behind.
The host does not tell if you win or lose,
Instead he decides to mess with your mind.

He opens a door, revealing a goat
And then he asks you 'Do you stay or switch?'
The answer to this, I don't want to gloat,
Can be found without duck, log, scale or witch!

Here is a problem about goats and car (chorus: goats and car!)
That confuses our good friend Araysar (chorus: Araysar!)
Here is a problem of doors and choices (chorus: doors and choices!)
In musical form, 'Bisi rejoices (chorus: he rejoices!)

Your initial pick, as we all do know
Makes you win a car, one time out of three
The host's trickery, that's the killer blow,
Does not change these odds by any degree.

With that clear in mind, you see what to do
to boost your chances at a Ferrari.
As obvious as three minus one is two
Switching wins the car two times out of three.

This was a problem about goats and car (chorus: goats and car!)
Made clearer for our good friend Araysar (chorus: Araysar!)
This was a problem of doors and choices (chorus: doors and choices!)
In musical form, 'Bisi rejoices (chorus: he rejoices!)


/bow
 
iannis

iannis

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We now have Swiss Rap in this thread.

Swiss rap.
















drop da baaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaass
 
Tuco

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Iannis_sl said:
I basically hate mythbusters for the gay format of their show. Every once in a while they'll have an interesting myth that they "bust". As in find an excuse to blow something up. But they always do 2 or 3 per show, and they always break them into 5 minute segments.

I mean fuck those hipster jackoffs. We're about to blow something up! followed by 10 minutes of watching the asian dude build a robot and talking about how cool it's gonna be to smash something with it.

Fuck that show.
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Yeah their show is unwatchable for me. The last one I saw was the breaking bad episode and they covered so little content over the duration of the show I had to fast forward it. And there's no real scientific discussion, it's just lowest common denominator gruel.
 
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