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/sci/ - Science & Math

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File: 11 KB, 371x318, VosSavant2[1].jpg [View same] [iqdb] [saucenao] [google]
3207108 No.3207108 [Reply] [Original]

A woman named Marilyn vos Savant (pic related), who according to Wikipedia has the highest IQ in the world, says this:

>Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?
>Answer: 1/3

I was intrigued by this because I could not figure out why this is correct. So, I ran a simulation, and I'm still getting the wrong answer. What am I doing wrong?

Simulation (python):
http://pas(REMOVETHIS)te2.org/p/1463885

>> No.3207119

>2011
>still think IQ matters above 120

I seriously hope you don't do this.

>> No.3207126

>>3207108 http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

The question is phrased in such a way it can be interpreted two different ways, but it Jedi mind tricks you into not realising it. People will argue for hours about the correct answer, when in reality they have both correctly answered different questions.

>> No.3207128

It's 50%. The first child is irrelevant.

>> No.3207131

possible cases:

Boy Girl
Girl Boy
Boy Boy

1/3

For a clear reason as to WHY it is 1/3, see the following:
http://en.wikipedia.org/wiki/Monty_Hall_problem

You are assuming more information than was given. When told there was one boy you assumed that one of the two children was a boy, and so it was 50/50 that the other was a boy. In reality either could be a boy, and either could NOT be a boy.

>> No.3207133

You have to randomly assign BOTH genders, then look at all families except those with two girls.

Don't just say "one's a boy" and then make the other random, which I assume is what you're doing.

>> No.3207137

girl boy
boy girl

I still don't understand how the order could possibly matter.

>> No.3207143

>>3207128
That's not how it works. Please read this article.
http://en.wikipedia.org/wiki/Monty_Hall_problem

The answer is 1/3, although it can be hard to see. Human minds are not naturally built with the tools needed to understand certain statistical situations.

>> No.3207144

children: X, Y

genders: M, F

possibilites:

MM, MF, FM, FF.

In this specific case (by wording) MF = FM as it doesn't matter which child (X or Y) is male as one of them IS (explicit by the sentence: "at least one of them is a boy").

Therefore, our universe of possibilities resumes to

MM, MF, FF.

Possibility of both being male = 1/3 .

smartest woman alive my ass, this is the living proof IQ means nothing. this problem isn't hard it's just puzzling due to wording.

>> No.3207154
File: 39 KB, 450x268, jackiechan.jpg [View same] [iqdb] [saucenao] [google]
3207154

>yfw if you think about it, it could be 1/3 or 1/2
>yfw your mind is full of fuck

>> No.3207158

>>3207137
Think of it as coins. If you were to flip one coin, you could get H or T. Then you flip a second coin, it could be H or T.

Now, lets examine every possible situation that could arise if you flip both coins at the same time.

The possible results are:
Coin1 H, Coin2 H
Coin1 H, Coin2 T
Coin1 T, Coin2 H
Coin1 T, Coin2 T

Now, afterwards, lets say I inform you that at LEAST one of the coins is tails. Lets remove the impossible. That leaves us with the following.

Coin1 H, Coin2 T
Coin1 T, Coin2 H
Coin1 T, Coin2 T

There is, as you can clearly see, a 1/3 chance if both coins being tails. Do you understand now? If not than I'm not even going to bother trying to explain again because I've made it as clear as possible, and you are either really really stupid or a troll

>> No.3207163

>>3207144
but the probabilities of MF and FM are only half of MM and FF.

>> No.3207167

>>3207144
Marilyn vos Savant is the quintessential MENSA type. The only thing her gamed up IQ is good for is for getting into MENSA.

You know how Donald Trump's public persona is that he a megalomaniacal financial genius? He's not actually good at business either, he just plays one on TV.

>> No.3207173

>>3207163
I mean, it should be MM, MM, FF, FF, MF, FM

>> No.3207176

>have high IQ
>do nothing with it
sage
sage
sage
sage

>> No.3207178

>A few months after the announcement by Andrew Wiles that he had proved Fermat's Last Theorem, vos Savant published her book The World's Most Famous Math Problem in October 1993.[16] The book surveys the history of Fermat's last theorem as well as other mathematical mysteries. Controversy came from the book's criticism of Wiles' proof; vos Savant was accused of misunderstanding mathematical induction, proof by contradiction, and imaginary numbers.[17]
lmao

>> No.3207179

>>3207144
You forgot that there are only two possibilities out of those three with, at least, one male; and with that prerequisite, only one of those two has two males. Thus, 1/2.

>> No.3207181

>>3207173
No, it shouldn't. There is only one possible configuration of results that would result in MM, and only one configuration that would result in FF. Conversely, there are two configurations of children that would result in one male and one female.

>> No.3207186

>woman
>intelligence

If there were ever a case for IQ tests being useless, I can't imagine a better one.

>> No.3207207

>>3207163
>>3207173

>In this specific case (by wording) MF = FM as it doesn't matter which child (X or Y) is male as one of them IS (explicit by the sentence: "at least one of them is a boy").

This is where this 'mathematical' puzzle becomes confusing, because you automatically tries to solve it interpreting the variables as human beings instead of simple mathematical variables, thus you think that which one is the male or the female matters when it actually doesn't.

ONE IS MALE, DOESN'T MATTER WHO.

See it as a purely mathematical problem in terms of variables and forget all the children, male, female, human or not, living organism or not and etc.

Think abstractly.

>> No.3207225

>Mr. Smith has a son and one unknown
>The probability the unknown is a boy=1/3???? WTF?

>> No.3207236

Isn't it...

2 C 1 / 2 C 2

>> No.3207249

why does everyone always say there are 4 possibilities?

there are 8 possibilities.

>> No.3207251

>Gardner initially gave the answer...1/3...but later acknowledged that the second question was ambiguous.[1] Its answer could be 1/2, depending on how you found out that one child was a boy. The ambiguity, depending on the exact wording and possible assumptions, was confirmed by Bar-Hillel and Falk,[3] and Nickerson.[4]

>> No.3207260

>>3207249
I'm getting six.

>> No.3207271

>>3207249
well that can be explained through your lack of mathematical knowledge beyond simple kindergarten mathetmatics

>> No.3207277

>>3207167
hay, don't criticize mensa!!1! i am in mensa becuz my iq is 189, your just jealous that you din't get in dumbass!!

~~proud mensa membor for 20+ years

>> No.3207278

>>3207260
we have 2 possible scenarios
1. first child is male

mm
mf
fm
ff

fm and ff are thrown out

2. second child is male

mm
mf
fm
ff

mf and ff are thrown out

so of the 8 results 4 are valid
mm
mf
fm
mm

so mm is 50%

>> No.3207282

>>3207131

Aren't Boy Girl and Girl Boy the same thing? I fail to see how order matters. The problem says nothing about the order in which the kids are born.

>> No.3207284
File: 56 KB, 294x313, DEAR-FAGGOT-TODAY-OP-WAS-A-DIARY.jpg [View same] [iqdb] [saucenao] [google]
3207284

>a woman
>IQ

>> No.3207292

>>3207278
you should change your tripcode because you're ashaming pascal's name and i don't think he would be ok (if he were alive) with you using his name around and spreading idiocy.

>> No.3207303

>>3207292
pascal invented game theory

>> No.3207310

>>3207278
Yeah, it's just that I wasn't counting the FFs as possibilities.

>> No.3207324
File: 36 KB, 225x212, godot.png [View same] [iqdb] [saucenao] [google]
3207324

Two possibilities:

Two boys
Boy and Girl

I don't understand why order would matter. Boy/Girl and Girl/Boy shouldn't make any difference going by what the question is asking.

>> No.3207325

>>3207310
wait, nevermind.

>> No.3207335

HURP DURP HAVE HIGHEST IQ MUST BE A SUPER EINSTEIN!

IQ is bullshit

>> No.3207337

>>3207207
I see both ways. My problem is that I can't prove either to be incorrect.

>> No.3207341

YOU DONT need to be smart to use fucking bayes formula or conditional probability, congrats on knowing how to use statistics 101 formulas you arrogant bitch.

>> No.3207347

>>3207335
>i'm too dumb to score above 160 on an iq test, so i go around saying it's invalid

>> No.3207359

>A woman named Marilyn vos Savant (pic related), who according to Wikipedia has the highest IQ in the world

and this resumes why i don't rely on wikipedia

>> No.3207362

>>3207282
>>3207324
It matters because you get double the results of MF/FM than you do MM or FF. If you were to flip two coins 100 times, for instance, you would get (on average) 25 HH 25 TT and 50 HT/TH. Follow?

>> No.3207375

>At least one of them is a boy

KEY
PHRASE

this means minimum outcome is one boy.
a single boy will ALWAYS be born for the purposes of this exercise.
This removes that child from ANY equation, because that child's sex is a known and unchangeable variable.

The probability of Mr Smith having TWO boys is 50%.

People who have trouble with word problems are idiots in their deductive reasoning.
Remove unnecessary elements and apply logic.

>> No.3207409

>(on phone with Mr Smith)

>Me: How many children do you have?
>Mr. Smith: Two
>Me: Is one of them a boy?
>Mr. Smith: Yes
probability of BB is now 1/3
>Me: Is the boy older or younger?
>(Mr. Smith Answers)
probability of BB is now 1/2 regardless of his answer.

Can someone please explain to me how this makes any sense at all?

>> No.3207411

>>3207375
>This removes that child from ANY equation, because that child's sex is a known and unchangeable variable.

No, it just means any equation that doesn't meet the requirement boys >= 1 is a contradiction.

So boy girl, girl boy and boy boy valid but girl girl is a contradiction and of the three that are valid all are equally likely and only in one of the three does boys = 2 so you have 1/3

>> No.3207416

>>3207411

boy girl and girl boy ARE THE SAME

ORDER DOESNT MATTER

>> No.3207419
File: 2 KB, 126x126, costanz.jpg [View same] [iqdb] [saucenao] [google]
3207419

>taking more than 2 seconds to come up with 1/2
>not putting yourself in the fridge otherwise

>> No.3207424

>>3207416
Please explain how boy then girl and girl then boy are not distinct outcomes.

>> No.3207430

>>3207375
Imagine that I flip two coins, look at them, and say "at least one is tails". Repeat as necessary, ignoring two head results. If you guess that the other is also tails, how often will you be correct? Around 33%.

>> No.3207457

HEY FUCKTARDS!

Instead of arguing about this like religious idiots, why don't you actually read up about it instead of just parroting the same shit over and over again?

See >>3207126

Being an arrogant fuckwit is annoying, but even more so when you're wrong. Take a few minutes to improve yourself and actually learn something instead of being a worthless vapid douche.

>> No.3207460

>>3207424

because the problem is asking the chances that both are boys

either one of the kids is a boy...or both are. whoever is born first is irrelevant.

maybe im missing something here but i dont see it. i feel like people are just overcomplicating things

>> No.3207458

>>3207409
It doesn't make sense because you're misunderstanding, and the probability doesn't change. By answering the question "older, younger, or both" he tells you the result. There is an equal probability of each of those answers, meaning a 1/3 chance of "both".

>> No.3207480

>>3207457
The wording is ambiguous, although the intent was for it to be interpreted so the answer was 1/3. Regardless, the argument persists because some people don't understand how the answer could ever be 1/3. While it's understandable why someone would initially come to the 1/2 answer, they should be able to comprehend why 1/3 is correct as well.

>> No.3207500

>>3207457
>religious idiots
LMAO. You think religious people are idiots? Then who created the universe, fucktard?

>> No.3207502

>>3207460
There are 100 sets of two children, 25 with two boys, 25 with two girls, 50 with one of each. If you pick a random set which turns out to have at least one boy, it's twice as likely to be one of each than two boys.

>> No.3207513

>>3207502
>>There are 100 sets of two children, 25 with two boys, 25 with two girls, 50 with one of each. If you pick a random set which turns out to have at least one boy, it's twice as likely to be one of each than two boys.

I was actually just about to write that in reply, almost word for word
nice, well-explained

>> No.3207514

Haven't read thread but..
4 options
1. First boy, second boy
2. First boy, second girl
3. First girl, second boy
4. First girl, second girl
exclude 4th option, 1/3 chance of both boys

>> No.3207536

Boy, girl, hermaphrodite.

>> No.3207544

>>3207500
-1/10

fail troll is fail

soniamdisappoint.jpg

>> No.3207546

>>3207502

But you're implying that it's more likely for a family with two kids to have one of each than two boys or two girls, which it isnt

>> No.3207560

ohlookitsthisthreadagain.png
it's a stupid example of conditional probability. 1/3 is correct, but in reality it's unlikely that you know there is a boy but don't know which one it is.

tldr; beginning stats faggots like to troll to feel smarter

>> No.3207574

>>3207546
Yes it is. Assuming equal probability of boy and girl, it's twice as likely. This is pretty basic stuff.

50 will start with a boy. Of those, half will then have a second boy and half will have a girl. So 25 BB 25 BG. The other 50 will start with a girl. Of those, half will have a second girl and half will have a boy. So 25 GG 25 GB.

>> No.3207580

>>3207131
The strange thing is that I read about the Monty Hall problem and understood it in 2 seconds, but I still can't seem to figure out this one, despite my seeing the similarities between the two.

>> No.3207684

* A man is walking with a boy.
* Man says the boy he is walking with is his son and that he has another child.
>Probability of other child being male is 1/3 at this point, according to Vos Savant
* Man says his son he is walking with is the oldest
>Probability of other child being male becomes 1/2
OR
* Man says his son he is walking with is the youngest
>Probability of other child being male becomes 1/2

^This is correct, right?

>> No.3208862

P(both are boys|at least one is a boy)=P(both are boys AND at least one is a boy)/P(at least one is a boy)=P(both are boys)/P(at least one is a boy)=(1/4)/(3/4)=1/3

Get your shit together, /sci/. Also, if anyone says "HURR, P(at least one is a boy) = 1 SINCE IT SAYS SO", again, get your shit together. P(at least one is a boy|at least one is a boy) is 1. P(at least one is a boy) = 1/4 in an unrestricted outcome space, since this is unconditional probability.