/sci/ - Science & Math

[Anonymous No.9962308]

Is it true that people who cannot ever seem to grasp the solution to this problem are categorically brainlets, and their opinions should subsequently be discarded?

[Anonymous No.9962310]

No, we should be patient with them and teach them over and over until they learn.

Think of humanity as a single organism, that may help you

[Anonymous No.9962320]

>>9962310

Although I have no proof, I am willing to bet that that "controversial" math problems like the Monty Hall problem can point out people with fundamental cognitive deficiencies, even after the answer is explained to them in full detail.

I'm not saying you need to have a high IQ or be a genius to get the solution, but those who fervently believe that it is 50:50 have some sort of mental blind spot where they think that they are more intelligent than they really are. Kind of like the Dunning-Kruger effect. It could be seen as a red flag. There are people who rely on flawed heuristics and flawed logic when it comes to abstract thinking.

[Anonymous No.9962328]

>>9962308
>caring about opinions at all

kys brainlet undergrad

[Anonymous No.9962337]

No, the problem is that boomers are opposed to teaching critical thinking and formal logic to elementary students.

[Anonymous No.9962878]

>>9962308
Its may be your fault for not explaining it in proper way.

Easly make number of doors possible much bigger and almost everybody get it, if not they are true brainlets beyond hope.

[Anonymous No.9963214]

>>9962310
this, get off your high horse.

I think the best explanation is imaging the problem with a 100 doors and eliminating 98. That tends to make sense to most people, myself included.

[Anonymous No.9963436]

>>9962308
I did not understand this before that pic, thanks OP!

[Anonymous No.9963448]

>>9962308
Human intuition is actually very bad at conditional probability in general, so it's not surprising so many people don't understand this at first.

[Anonymous No.9963565]

>>9962337
I posted about this before, but I didn't have to do mathematical proofs until COLLEGE. And a 300 level course at that.

Now, I did grow up in rural Arizona, a place with an absolute dogshit education system, but it really is amazing how terrible they prepare students for any sort of critical thinking in this state (and I'm sure many places in the country).

[Anonymous No.9963740]

>>9963565
Same story in California. We did have "finite math" (basically discrete math lite) in high school, but that was geared for the mediocre students, the ones better than remedial students but worse than those who took the calculus/statistics route.

Google "Lockhearts Lament" a short essay on the topic.

[Anonymous No.9963762]

>>9962320
>but those who fervently believe that it is 50:50 have some sort of mental blind spot where they think that they are more intelligent than they really are

The reverse is true though. The 50:50s are unironically right unless the problem is stated in a very rigorous and unambiguous way so that the possibility of the host having any influence over the outcome is excluded, a boobie prize being revealed and then a switch being offered are guaranteed and the contestant's choice is also limited specifically to the initial 1/3 choice and the subsequent binary choice to switch. Unless these conditions hold, the chances being 50:50 is the more accurate answer in most statements of the problem.

People who think the reveal of the goat itself, regardless of how it happens, is what makes the swap 2/3 are the true brainlets, as they are basically basing their understanding of the problem off the authority of what they think smart people think, even though people who are actually capable of thinking through the problem know that this is actually false and misleading.

[Anonymous No.9963775]

>>9963448
http://opinionator.blogs.nytimes.com/2010/04/25/chances-are

breast cancer example, correct answer surprises most people

[Anonymous No.9964068]

>>9963775
>mfw I read 0.8 as 80% the first time around

[Anonymous No.9964083]

>>9962328
>caring about things is for brainlets now
kys self-taught innovator/inventor lmao

[Anonymous No.9964084]

>>9963775
>The trick is to think in terms of natural frequencies (8 out of 100 people), rather than the more abstract notions of percentages (8% of people)
I refuse to balieve that the average person is so retarded that you have to explain this to them. I mean Jesus Christ, its literally what percent, per-cent, means, or is the hard part realizing that 4 out 50 people is the same as 8 out of 100? do these people also struggle with simplifying basic fractions?

>Notice two simplifications in the calculation above. First, we rounded off decimals to whole numbers.
>Of these 8 women with breast cancer, 7 will have a positive mammogram.
>Really we should have said 90 percent of 8 women, or 7.2 women, will have a positive mammogram.
>So we sacrificed a little precision for a lot of clarity.
People cant even handle decimals? who are these people? Except for one guy I know who is legitimately mentally retarded, I cant imagine someone not being able to understand this without having it specifically explained to them.

[Anonymous No.9964092]

This thread is a bunch of dudes masturbating through words.

[Anonymous No.9964093]

>>9964084
You'd probably be alarmed by the amount of people in rural areas who would respond with
>HAHAHA what happened to that .2 of a person did she get in a BIG CAR ACCIDENT
>you can't have .2 of a person
>I will now ignore the entire study, mammograms are for pussy city girls

[Anonymous No.9964096]

look... brainlets exist. mostly through no fault of their own. just leave them be. "any man can learn anything" hahaha just no. the enlightenment was a mistake. send all of the peasants back to the fields where they will be happy to be illiterate toilers instead of chasing the dream that everyone can be an Einstein if we only sufficiently tweak and fund the public education system.

[Anonymous No.9964101]

>>9963762
is this a troll?

[Anonymous No.9964112]

>>9963762

lmao you can't be serious

[Anonymous No.9964146]

>>9964093
But I live in a rural area. Most people I know there are farmers and never went to uni, and don't have trouble with understanding that a fraction is.

[Anonymous No.9964147]

>>9962308
are you delusional or retarded? give someone enough training and/or chemical calibration (i.e. adhd meds) and they can solve problems they couldn't before solve. the brain is incredibly plastic

typical /sci/-fi-er

[Anonymous No.9964188]

>>9964147
Neuroplasticity has nothing to do with taking adhd "meds". You're not "calibrating your brain chemistry". That's TED talk level pseudoscience. Taking ADHD "meds" is just taking drugs. They are very similar to cocaine. And sure, when you take cocaine, obviously your brain functioning will change, that's why people take drugs. But it has nothing to do with "plasticity".

Also, the brain really isn't that plastic. The potency of neuroplasticity is really overrated by pop science. If someone has down syndrome, it doesn't matter how many learning exercises they do or how much Adderall they take; they are not going to understand calculus

[Anonymous No.9964191]

>>9964147
>lol just overclock your brain bro, I saw it on Lucy bro

[Anonymous No.9964190]

>>9962308
This may be the case in mathematics but in the real world it's 50/50. Suck it up nerd

[Anonymous No.9964253]

>>9964112
>>9964101
I can guarantee that neither of you are capable of working through the problem.

Here Monty Hall discusses the problem and the ambiguities it has and Marilyn vos Savant agrees that, given the host is given freedom to change his actions based on the circumstance, that the reveal of the goat will not necessarily result in the 2/3 win chance of switch.

https://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doors-puzzle-debate-and-answer.html

This paper discusses analyses implications of this freedom and shows that the host, in playing 'optimally' given that he has the freedom to refuse to reveal the location of a dud prize and allow a switch, has reason to play and offer choices in such a way that ultimately results in a 1/2 chance of the contestant winning regardless of whether they stay or switch. It also explains why adding more doors to the problem intuitively makes the choice to switch "make more sense".

www.mdpi.com/2073-4336/8/3/31/pdf

If you think that the reveal of the goat, unconditionally and regardless of the circumstances, naturally gives you a 2/3 chance to get the car on switching, then you do not understand how to reason through probability problems and have duped yourself into thinking you are smarter than the 'idiots' because you and not honestly thinking about the problem carefully enough.

If you disagree and believe you can refute the reasoning and analysis given, please by all means do so.

[Anonymous No.9964261]

>>9964253
what you're talking about is an entirely different, "second" version of the Monty Hall problem. the abstract of the pdf hints at that.

in the classic version, the one that I and everyone else I know has heard, the host has no influence whatsoever. the host is a complete unknown. there's nothing about giving the contestant the opportunity to switch only in certain circumstances. in fact, i've seen the problem reformulated outside of a game show setting and with no host at all.

[Anonymous No.9964271]

>>9963214
Why would you eliminate 98 and not just 1 more door on the second round of guesses?

[Anonymous No.9964278]

The people who don't understand this are unironically stupid but who cares? There are even stupider people too.

The reason they don't understand is because they can't even notice that there is significance in the fact that he opens a goat every time.

They don't understand that there is significance in the fact that they picked with a 1/3 chance of winning regardless of what happens after they picked. The chance only changes if they change because their initial choice will always be a 1/3 chance.

They are unironically dirt stupid to never figure this out, but who cares, it's not important.

[Anonymous No.9964283]

>>9964278
>The reason they don't understand is because they can't even notice that there is significance in the fact that he opens a goat every time.
>he opens a goat every time
>opens a goat

[Anonymous No.9964289]

>>9964283
Listen here kiddo, this ain't /lit/, and not only that, but my quality of typing is impeccable.

You fell for an obvious trap in my typing, you think that the only way to say it was "opens a door that reveals a goat" but no, no, no, you were wrong.

"Opens a goat" refers to him opening something with a goat lying behind it.

[Anonymous No.9964293]

>>9964289
>"Opens a goat" refers to him opening something with a goat lying behind it.
idunno about that

>my quality of typing is impeccable
i agree with this. i just have a moral problem with attempting to open up an animal while it's living

[Anonymous No.9964298]

>>9964271
so you only have a choice of "switch or stay", like before. instead of turning it into "switch to one of these many options, or stay"

[Anonymous No.9964301]

>>9964293
>seriously being this pedantic about what anon meant, even when it was obvious to infer
High school detected

[Anonymous No.9964302]

>>9964293
lol

[Anonymous No.9964304]

>>9964253
>given the host is given freedom to change his actions based on the circumstance
>given that he has the freedom to refuse to reveal the location of a dud prize and allow a switch
The fuck is this? obviously if you change the problem the answer changes. The original problem is completely well defined and I dont know if the people struggling to understand it arnt native/good English speakers, or just too autistic to understand basic communication.

[Anonymous No.9964307]

>>9964261
>what you're talking about is an entirely different, "second" version of the Monty Hall problem

This isn't entirely true. The 'first' version of the Monty Hall Problem quite explicitly involves both the host and the contestant making free choices (in fact, in the original paper, it's the CONTESTANT who requests the possibility of switching) that we have no reason to believe follow a pre-set script restricting their actions, and the problem in Marilyn's statement also doesn't specify that the host's actions are predetermined, and so potentially allows for the POSSIBILITY that the host COULD HAVE decided not to reveal the goat, even though he happened to in your case. That "the host has no influence whatsoever" is an assumption unless the sequence of events he follows is made explicit in advance or guaranteed, which wasn't actually the case in Marilyn's version and she admits that it was in fact ambiguous, and that the the 2/3 chance for switching can't be assumed without further qualification.

So what you call the 'original problem' is actually a secondary, derivative problem that arises from models of the actual original problem in which the host's actions are assumed to be deterministic. Assuming that, because Monty shows you the goat, he always shows everyone the goat, is a dangerous assumption that could easily let you get conned, as Monty himself explained.

>i've seen the problem reformulated outside of a game show setting and with no host at all

In which case they're reformulating the 'derivative problem' where free actions are explicitly disallowed.
Original paper (in which I actually DO think that switching is the better idea, given the particular subtleties of the problem):

https://www.jstor.org/stable/2683689

[Anonymous No.9964310]

>>9964253
>www.mdpi.com/2073-4336/8/3/31/pdf
Thats not the monty hall problem you retard, its an extension of it that allows more solutions based on the exact conditions assumed, it even says so in the fucking abstract.

[Anonymous No.9964312]

>>9964307
>In which case they're reformulating the 'derivative problem' where free actions are explicitly disallowed.
gameshow hosts dont have any free actions, wtf, they have to play by a regit set of rules. they are only there to make the process more interesting. Im just going to assume this is bait now and leave the argument.

[Anonymous No.9964318]

>>9964307
alright, that's all fine. i can admit it's interesting to think about what the host might do too.

as long as we agree on how the logic/math is working here. i don't care which version is which

[Anonymous No.9964329]

>>9964298
But it's still switch or stay even with 98 doors

[Anonymous No.9964369]

>>9964304
>The original problem is completely well defined

It's not and there is no controversy about this. The original problem is full of ambiguity and I've both posted my reasoning and referred to the arguments and comments of the major people involved in the creation and popularization of the problem, who attest to the ambiguity, which doesn't specify a formula for the host to follow and only gives an instance of the host interacting with the contestant, which implicitly allows the possibility of this freedom to not reveal.

>>9964310
>it even says so in the fucking abstract

You're misreading or making assumptions, the paper explicitly says that it is modeling ambiguities inherent to the actual problem statement in its introduction, and only proposes the 'n door problem' as an alternative formulation. It states:

>"It is important to recognize; however, that in the scenario presented above, as in vos Savant’s columns, Selvin’s articles, and many other formulations of the problem, it is unclear whether Monty must reveal a goat and allow Amy to switch."

However, it also then says:
>"However, their subsequent analysis and solutions imply that this is an implicit condition on the problem."

Implying a distinction between the actual problem formulation (which is ambiguous) and the 'intended' problem implied by after the fact analysis of the scenario by the authors. The argument is that it is completely reasonable, on hearing the problem statement to assume that the contestant has a 50:50 chance at best unless they have explicit reason to believe that the host couldn't possibly be deliberately tricking him, and that this is fact the most reasonable thing to believe. Pretending that the problem statement, as presented, implies a 2/3 chance to win on switch is dishonest and misleading.

[Anonymous No.9964398]

>>9964369

[Anonymous No.9964411]

>>9964369
There are some fundamentally wrong assumptions about the game show. The choice is offered as a twist on the drama of fate: your hand, your fate. The contestant winning will not cause adversity to any successful game show.
Suppose that the show is based around optimally retaining the prizes - not ratings because we are autistic - what percentage of the time must the host offer the switch when a person has picked the goat curtain?
It is pretty obvious the host can't only offer the switch when the contestant happens to pick the curtain with the car behind it.

[Anonymous No.9964452]

>>9964369
>it is completely reasonable, on hearing the problem statement to assume that the contestant has a 50:50 chance at best

i'm not sure i follow where 50:50 at best comes from; at best, the host might be playing fair so that it's 2:1.

or really, at best, the host could only present the switch opportunity when the first choice was wrong, making it a 1:0 win, and at worst, could only present the opportunity when the first choice is right, for 0:1.

[Anonymous No.9964614]

>>9963740
Yes! The beauty of doing proofs and playing in abstractions and ideas is something that, frankly, I'm a bit angry I was denied for most of my young life. I've come to love mathematics, but only in the last few years.

If I ever have children, I feel it would be important to home school them on mathematics. Real mathematics. Because our education system is intent on viewing math as a mere tool. A trend that, frankly, most subjects are being destroyed by, but math more than most.

[Anonymous No.9964746]

>>9964369
You are focusing on the wrong part of the problem and completely missing the point of this thread. forget the monty hall problem then take Bertrand's box paradox.

>There are three boxes:
>a box containing two gold coins,
>a box containing two silver coins,
>a box containing one gold coin and a silver coin.
>after choosing a box at random and withdrawing one coin at random, if that happens to be a gold coin, whats the probability of the next coin drawn from the same box also being a gold coin.

This is basically the same problem but with 0 possible ambiguity in the problem statement, yet a lot of people will not understand the solution and argue its 1/2 instead of 2/3. Whats what the threads about, not retards not being able to understand a very specific word problem.

[Anonymous No.9965335]

>>9962308
the odds are still one in two, regardless of whether you switch. This meme needs to die.

[Anonymous No.9965339]

>>9964746
lol, wut?
this is ridiculous, its not 2/3s
Thats like saying the chance of getting xy chromosomes are 1/4.

[Anonymous No.9965342]

[Anonymous No.9965353]

>>9962308
you guys are fucking retarded.
this is called the gambler's fallacy.

[Anonymous No.9965373]

2/3

[Anonymous No.9965468]

>>9965373
And why does this not account for picking the other door with a goat? Its not like these are glass doors and you can choose to pick the car.

[Anonymous No.9965484]

>>9965468
It's pretty self explanatory. That option is shown in the 6th outcome. I don't know why you can't see it.

[Anonymous No.9965490]

>>9965484
Of course i see that. but thats not how flow charts work. it says if you change your door choice you instantly get a car, it does not say go choose another door.

[Anonymous No.9965519]

>>9965490
But that's what the first choice in blue shows, the choice to stick or change is clearly stated after the initial choice.

[Anonymous No.9965581]

>>9965373
>>9965342
felt like a brainlet until i saw these two.
thanks! the 2nd one is especially clear

[Anonymous No.9965644]

I have 3 doors. Behind the doors are these 3 prizes:
•$1,000,000
•$2,000,000
•$3,000,000

>OUTCOME1
>pick 1
>2 is removed
>stay get 1, switch get 3

>OUTCOME2
>pick 2
>1 is removed
>stay get 2, switch get 3

>OUTCOME3
>pick 3
>1 is removed
>stay get 3, switch get 2

>OUTCOME4
>pick 3
>2 is removed
>stay get 3, switch get 1

Two win by stay scenarios.
Two win by switch scenarios.
Four outcomes.

Its 50/50

[Anonymous No.9965667]

>>9965644
Great, now you have made up your own hypothetical and it's no longer the Monty hall problem. This is why we need /sci/. Innovators like this guy.

[Anonymous No.9965900]

Theres a 66% chance to win by switching, but is there a 100% guaranteed winning method without already knowing where the car is?

[Anonymous No.9965907]

>>9965900
easy. open two doors.

[Anonymous No.9965918]

Did anyone who won a goat actually get to keep the goat?
If they wont even give you a goat why would you assume they'd give you a car.

[Anonymous No.9965929]

>>9965918
ye like, what if I want a goat. Thats a 2/3 chance to win a free goat. That goat could on to become one of your best friends, you know? The goat is a living being, and has hopes and dreams. Cars aren't alive. Cars don't have feelings. You can't talk to a car. You can't pet a car. You can't take naps with a car. You can't let a car eat little nibbles out of your hand. You can't fuck a car. You can't milk a car. The car is totally replaceable, but the goat could be your little buddy forever.

[Anonymous No.9965931]

>>9965929
>You can't fuck a car

[Anonymous No.9966529]

>>9965339
God you are retarded.

See what I mean? people cant grasp this even though there is no ambiguity.

[Anonymous No.9966542]

>>9965929
You could sell the car and buy many goats

[Anonymous No.9966669]

>>9965373
This is stupid because it makes no assertion that you have been revealed any additional information. In order for your 2/3 conclusion, you must be shown a goat before the switch, otherwise you are omitting the option that you switch and end up with a goat. Im telling you this so you understand why some people may not understand

[Anonymous No.9966842]

>>9966669
>blah blah idiot rambling
lrn2read

[Anonymous No.9966950]

>>9965490
Monty opens a goat door before offering you the choice.

[Anonymous No.9968119]

>>9963762
/thread

[Anonymous No.9968140]

>>9963762
>I pick door with 66% chance of being goat
>Wilderberger sensei says 2/3 is not a number
>A door that is independent of this door opens
>now my door has 50% chance of being goat
>pi is not a number

[Anonymous No.9968149]

>>9965929
>>9965931
Guarantee some aut/o/s probably do these to/with their cars

[Anonymous No.9968258]

If picking the car to reveal goat1 and picking the car to instead reveal goat2 are the same single event (1/2 + 1/2), then picking goat1 to reveal goat2 and picking goat2 to reveal goat1 should also be considered the same event (1/2 + 1/2).
Instead, it is implied to be twice as likely to choose a specific goat over the car, and half as likely that a specific goat will be revealed if the car were chosen.

Do you understand that probability is not quantum probability, where quantum probability gets you closer to the practical answer? there are 4 possible outcomes.
>1. Pick goat1, reveal goat2, switch win
>2. Pick goat2, reveal goat1, switch win
>3. Pick car, reveal goat 2, switch lose
>4. Pick car, reveal goat 1, switch lose

[Anonymous No.9968477]

>>9962308
All of them do loose.
Who tf wanna drive a gay smart?

[The Lord No.9968547]

What is the real Monty Hall problem?
If you go back and count the wins and losses on the show, do the statistics conform to the solution?

[Anonymous No.9968577]

>>9965339
Absolutely not. Remember, your father and mother each contributed one sex chromosome to you. Your father has one X and one Y chromosome, and therefore you half a 1/2 chance of getting either, leading to a chance of you getting XY or XX 1/2. This is because the probability of receiving one of your father's sex chromosomes is independent of the reception of your mother's sex chromosomes, which, by the way, can only provide an X chromosome.

This is probably confusing to you because either your mother's egg or father's sperm cell retained more than one copy of chromosome 21.

[Anonymous No.9968597]

>>9968258
why would you be more likey to pick car than any particular goat if there are three doors and one is chosen at random?

[Anonymous No.9969586]

>>9968597
Why would you be more likely to pick either goat instead of the car?
The game isn't
● ¤ □ > ●□ > ○■
● ¤ □ > ●□ > ○■
○▪□ > ▪□ > ¤ ■
○▪□ > ▪□ > ¤ ■
○ ¤ ■ > ○■ > ●□
○ ¤ ■ > ¤ ■ > ▪□

the game is
● ¤ □ > ●□ > ○■
○▪□ > ▪□ > ¤ ■
○ ¤ ■ > ○■ > ●□
○ ¤ ■ > ¤ ■ > ▪□

[Anonymous No.9969682]

>>9969586
Simplified
●○□ > ●□ > ○■ pick goat1, reveal goat2
●○□ > ●□ > ○■ pick goat1, reveal goat2
○●□ > ●□ > ○■ pick goat2, reveal goat1
○●□ > ●□ > ○■ pick goat2, reveal goat1
○○■ > ○■ > ●□ pick car, reveal goat1
○○■ > ○■ > ●□ pick car, reveal goat2

why should it be twice as likely to pick goat 1 over the car? Its not. Its twice as likely to pick A goat over the car, but each goat is still only 1/3.

So it should be
●○□ > ●□ > ○■ pick goat1, reveal goat2
○●□ > ●□ > ○■ pick goat2, reveal goat1
○○■ > ○■ > ●□ pick car, reveal goat1
○○■ > ○■ > ●□ pick car, reveal goat2

AKA
●•□ > ●□ > ○■ pick goat, reveal a goat
>switching wins
○•■ > ○■ > ●□ pick car, reveal a goat
>switching loses

[Anonymous No.9969713]

>>9966669
It does make the assertion. Because beforehand, if you chose a goat for example, switching doesn't mean you get a car, it means you could also get another goat. However, after the goat door is opened, you cannot end up switching from one goat to the other. So now it becomes that whatever you originally selected, you will get the opposite if you switch. So it happens to be that 2/3 times you chose the goat, so now that switching cannot land you to another goat, 2/3 times you will switch to the car. The assertion is there it's just not explained.

[Anonymous No.9969716]

>>9962320
That has nothing to do with intelligence though. It's just related to a inherent human cognitive bias. The human brain is not "programmed" to understand basic probabilities it is "programmed" to reject things it disagrees with though. The only solution to this is to teach kids to be humble and to not categorically refuse proof when they're proven wrong.
As for what you said I'm sure you're right that it could be used as a way to determine whether someone has a" blind spot" like you said.

[Anonymous No.9969823]

>>996958
found the zodiac killer

[Anonymous No.9969827]

>>9969586
found the zodiac killer

[Anonymous No.9969852]

>>9969827
Symbols built into smartphones