Hey, some guy just came up to me and said "I have two kids,

There's no way to tell because there are far to many variables affecting the sex of a child

>>8204348
That's completely spot on. Le reddit doesn't seem to think so.

https://www.reddit.com/r/math/comments/4spwm1/in_the_famous_question_i_have_2_kids_one_is_a/

This shit is hilarious.

>>8204355
>/r/math

if you want to suppose that it's a perfect system it would be a 3/4th chance of being a boy and a 1/4th chance of being a girl

tell me that's the conclusion they came to I don't want to look

0.5, assuming the two children are not identical twins

>all these idiots
the question isn't asking for the probability of the other child being one sex, but
>what would you wager
in this case, the only correct answer is "as much money as I have on hand", because the probability is 0.5 for the other child, and the expected value for this bet is maximized when you bet as much as you possibly can

>>8204368
>assuming the two children are not identical twins

So you'd factor in the 1 in 67 chance that this might have occurred, which would bias the result towards the other child being a girl in the case you wanted to consider this?

>>8204373
The "maximized expected value" is zero.
(Assuming the payout is 1-1.)
It's straight even-odds gambling, not a good bet that one should max out.

>>8204380
>The "maximized expected value" is zero.
ah, you're right, i fucked up how bets work

you're right, you shouldn't bet anything.

>>8204379
yes.

>>8204360
You're joking, right?

There's a 2/3 chance the other is a boy.

>>8204387
let's enumerate the possibilities

>two children
>at least one is a girl

>first child is definitely a girl
>first child is a girl, second is a girl
>first child is a girl, second is boy
1/2 chance the "other child" is a girl

>second child is definitely a girl
>first child is a girl, second is a girl
>first child is a boy, second is a girl
1/2 chance the "other child" is a girl

P(other child is a girl) = 0.5 * first case + 0.5 * second case = 0.5
P(other child is a boy) = 1 - P(other child is a girl) = 1 - 0.5 = 0.5

>>8204390
The possibility of BG, GB, and GG. These three have equal likelihood. 2/3. This is an elementary problem in conditional probability.

File: boysgirls.png (14KB, 454x388px)

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/thread

File: boysgirls.png (14KB, 505x316px)

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>>8204477
sorry guys its really late......

File: 2016-07-14-200617_868x307_scrot.png (43KB, 868x307px) Image search: [Google]

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>>8204540
>>8204477
the fuck is with this shitty naming, fucking mathematicians

>>8204548
whats wrong with it? not even sure if that image is supposed to be a good or bad example....

>>8204454
>These three have equal likelihood. 2/3.
Why? Wouldn't this only apply if there was some kind of selection process that only accepted families with girls and specifically ignored those without? How would that result from some guy telling you the gender of one of his kids?

>>8204355
>/r/math
>math
Naturally you're going to find a high concentration of delusional faith in statistics, despite any heuristic you come up with being naive and lacking any input from, or control for, real world variables. Variables that a re important and an inform your heuristic to much greater accuracy depending on the level of information available.

I swear, I don't know if math makes people stupid, or if stupid people gravitate towards using math as proof of their stupid assertions. This is as bad as that numberphile video on using statistics to weigh the probability you're actually sick. Which is again, fine in a vacuum, but otherwise a uselessly naive heuristic.

File: Capture.png (6KB, 1074x90px) Image search: [Google]

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>>8204548
How verbose.

>>8204624
How ugly.

>>8204340
anyone have the ogremagi multicast gif of op's pic?

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>>8204644
nvm i found it

>>8204340
I would wager every scrap of money I could gather. You are only asked to guess, not to guess correctly

>>8204596
>or if stupid people gravitate towards using math as proof of their stupid assertions

If by stupid, you mean socially naive, than probably. A decent number of otherwise sound of mind people have been duped into believing statistical nonsense though. See people not understanding how the Monty Hall problem depends on the options the host has and how that conditions the likelihood of the outcomes, so they justify their flawed ideas through the "what if there were 1000 doors!" scenario without understanding how that changes their intuition.

File: calvin-hobbes-loophole.png (23KB, 401x510px)

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>>8204658

>>8204340
>Hey, some guy just came up to me and said "I have two kids, and I'll tell you that one of them at least is a girl. What would you wager that you can guess whether my other child is a boy or a girl?"
>Wut do?

Ask him the odds he's willing to wager at.

>>8204348
>There's no way to tell because there are far to many variables affecting the sex of a child

You are a god damn quitter.

There are also many variables affecting what names people have and yet I'm willing to wager quite a sum of money that your name isn't wsdcvgthytraffdabgrwdfsfdntajmaywgdhavvdwtt, despite that actually legally being a valid name in America.

>>8204590
>Wouldn't this only apply if there was some kind of selection process that only accepted families with girls and specifically ignored those without?
Because he applied a condition. If the guy said "I have two kids. What is the younger one?" it's 50/50. The only possible combinations are BB, BG, GB, GG. If the guy said "I have two kids. At least one is a girl", then that removes the BB option as being a possibility. You only have 3 options to work with. That's how conditional probability works.

The chance is 50/50 you tards.

It doesn't change based on the sex of the children you've already had.

>The gun get reloaded multiple times a day.

>>8204379

Yes.

>>8204891
>You only have 3 options to work with. That's how conditional probability works.

But this doesn't factor in that having two girls would make the guy more likely to say "At least one is a girl" in the first place, as opposed to "At least one is a boy", since, after all, in order to make that statement he'd have to select one of the kids in order to make the statement about their gender in the first place. If he had a boy and a girl, than there's a 50% chance that he'd say the latter instead or the former, while with two girls there a 100% chance of the former, given he chooses to say a gender. The fact that you eliminate the BB option is not enough, the guy's statement skews the probability so that it's more accurate to say that the odds are 50:50. All three remaining options do not have equal likelihood.

Now, if YOU had asked him if he had any girls, and he said yes, then that would simply eliminate the BB case without otherwise biasing the result. This would result in the chanced of it being a boy being 2/3 and is effectively equivalent to your 'elementary problem'. Who asks and tells who what completely changes the problem.

>>8204940
>this is what a brain tumor looks like in the form of a forum post
nice "reasoning" you got there, bro

anyway, this is fucking babby probability stuff and can be done in <5minutes in any programming language. I did it in matlab real quick


# we create a bunch of families with two children
senpaitachi=[];
for N=1:100000
> #0=boy 1=girl
> senpaitachi=[senpaitachi [round(rand(1))+round(rand(1))]];
end

#families with at least one girl
fams_girl=senpaitachi( senpaitachi > 0 );
#out of those families the families that have two girls
fams_twogirl = fams_girl( fams_girl == 2);

prob=length(fams_twogirl)/length(fams_girl)


>prob = 0.33363

>>8204990
>/sci/ changes "F A M S" (short for families) to "senpaitachi"
wat. why

>>8204990
That proves absolutely nothing, since you're selecting the families with at least one girl out of the total population and not eliminating half of those who have one boy as well. This isn't accurate to the problem, and it assumes that somehow, there is some process simply selecting families with girls, which would make no sense for the father to do.

A father of two boys would never think to himself "I should tell someone that I have at least one girl" then hesitate and decide not to when he remembers that he actually has two boys. That's the kind of thing your program implies is happening. The scenario makes much more sense if the father has decided to disclose the gender of one of his children (implying he has chosen a specific child) and then tells you what that happens to be. It's equivalent to him saying "the oldest of my two children is a girl", or you asking "is your oldest child a boy or a girl?", and conveys only minimal information about the other child.

Please, I beg of you, think this through yourself. Senpaitachi.

I hate all of you.

>>8204990
>Comp sci undergrads

Why don't you go take a probability class ?

>>8205031
>you're selecting the families with at least one girl out of the total population and not eliminating half of those who have one boy as well
literally wat.
half of wat? families with at least one boy are half of what number precisely?

also if you dont agree with my simulation, give a better one. (if you cant program it can be pseudocode)

>>8205037
who says I havent already taken prob and stats?

but since some people seem to be resistant to verbal reasoning, I suggested modelling this (trivial) problem in a program and look at the numbers that come out.

if you think mathematicians dont routinely do number crunching / numerical examples to check their reasoning, you clearly are an edgy 15-year old high-school outcast who fancies himself above-average intelligence because he spends his free time shitposting on a hungarian sewing-maching-review forum

>>8205037
the numbers dont lie man, and since half you guys apparently cant be convinced by verbal reasoning someone had to come up with actual proof.

>>8205053
>>8205057
It doesn't matter when you don't model the situation right.

The probability of the second child being a girl knowing the first child is a girl is the probability of both childs being a girl divided by the probability of the first child being a girl, that is 1/4 * 2 = 1/2

The probability of the second child being a boy knowing the first child is a girl is 1-1/2 = 1/2

>>8204340
depends if fraternal or identical twins are more common I suppose

>>8204624
Gorgeous what language is it? Also is it just taking advantage of unicode in variable names?

>>8205066
the question is not if i take two children, what are the odds for both of them to be a girl, in which case the chance for the first child would be 50/50 and 50/50 again for the second. the question is, if one of them IS a girl, then what is the chance that the second one is a girl too.

And to that, the answer is 1/3.

>>8205066
>second child
>first child
no, the problem stated does not differentiate between first and second child. you're making stuff up.

also how can any probability of anything ever be 2? (as in your calculation)
language sucks for math, and you in particular suck at language.

please give pseudocode that will count stuff over a series of trials and give a probability that will converge to your answer, so others can unambiguously understand what the fuck you're on about

inb4 you cant because you dont even understand what you're saying

https://en.wikipedia.org/wiki/Boy_or_Girl_paradox

>Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls?
>Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?

First one is 1/2, second one is ambiguous as per references [3], [4], and [5] in the above wikipedia article.

/thread

>>8205042

>half of wat? families with at least one boy are half of what number precisely?
Those which have exactly one boy.

The total number of fathers who could have decided to tell you the gender that one of their children is is the implied problem space (if not explain how it could have been otherwise, why would a father tell you this info and how would he decide to do so?). Since a father can't decide to tell you he has a girl if he has two boys, that is eliminated from that problem space. A father with two girls will always say that he has at least one girl. A father with one of each could have chosen either way, but is half as likely to have told you that he had a girl compared to one with only girls.

>also if you dont agree with my simulation, give a better one.

import std.stdio;
import std.math;
import std.random;

enum gender { boy, girl };

void main()
{
const NumFamilies = 1000;
gender[2][NumFamilies] families;

for (int ii = 0; ii < families.length; ++ii)
{
families[ii][0] = cast(gender)(uniform(0, 2) % 2); //Random uniform value that is 0 or 1
families[ii][1] = cast(gender)(uniform(0, 2) % 2);
}

int numRemaining = 0;
gender[2][NumFamilies] familiesRemaining;
int[NumFamilies] childSelected;
int whichChild;

for (int ii = 0; ii < families.length; ++ii)
{
whichChild = uniform(0, 2)% 2;
if (families[ii][whichChild] == gender.girl)//Selects families where the randomly selected child is a girl
{
familiesRemaining[numRemaining][0] = families[ii][0];
familiesRemaining[numRemaining][1] = families[ii][1];
childSelected[numRemaining] = whichChild;
numRemaining++;
}
}

real girlCounter = 0;
real boyCounter = 0;
for (int jj = 0; jj < numRemaining; ++jj)
{
if (familiesRemaining[jj][childSelected[jj] ^ 1] == gender.girl)//If the other child is a girl
{
girlCounter += 1;
}
else
{
boyCounter += 1;
}
}
[spoiler][/spoiler]
writeln("There were ", girlCounter, " girls and ", boyCounter, " boys.");
}

>>8205080
Mathematica and yes, the notebook interface supports the use of a lot of special characters.

>deliberate exploitation of ambiguity for a troll thread
nice one OP

>Specifically, Gardner argued that a "failure to specify the randomizing procedure" could lead readers to interpret the question in two distinct ways:
>From all families with two children, at least one of whom is a boy, a family is chosen at random. This would yield the answer of 1/3.
>From all families with two children, one child is selected at random, and the sex of that child is specified to be a boy. This would yield an answer of 1/2.[4][5]

>>8205159
>enum gender { boy, girl };
>binary gender

>>8204454
But why do BG and GB matter if there's no reason to assume that the genders of children are dependent events?

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Solution in Emacs Lisp

http://pastebin.com/raw/rWzUWYfs

;; "I have two kids, and I'll tell you that one of them at least is a girl. What would you wager that you can guess whether my other child is a boy or a girl?"

(require 'cl-lib)

(defun average (x y)
(/ (+ (float x)
(float y))
2))

(defun make-n-kids (n)
(if (zerop n) '()
(cons (elt '( )
(random 2))
(make-n-kids (1- n)))))

(defun make-at-least-one-girl (count)
(let ((kids (make-n-kids 2)))
(if (member ' kids) (list kids count)
(make-at-least-one-girl (1+ count)))))

(defun prob-male-with-one-girl (n-tries probability-male)
(cond ((zerop n-tries)
probability-male)
(t (prob-male-with-one-girl (1- n-tries)
(average probability-male
(let* ((kids (make-at-least-one-girl 0)))
(average (if (member ' (car kids)) 1 0)
(cadr kids))))))))

(defun prob-male (n-tries)
(let* ((lst (cl-loop for x from 0 to n-tries
collect (make-at-least-one-girl 0)))
(non-one-girl (apply #'+ (mapcar #'cadr lst)))
(cnt (length lst))
(cnt-males (length (cl-remove-if-not (lambda (x)
(member ' x))
lst))))
(/ (+ (float cnt-males)
(float non-one-girl))
(float cnt))))

(prob-male 100000) ;; => 0.334...