kubikulann
Joined: Jun 28, 2011
• Posts: 905
May 28th, 2014 at 1:39:32 PM permalink
Quote: AceTwo

I did the calculation and he is he right 100%, on the first problem the ratio stays 1:1

OK. So you used brute force calculation for one example (p=50%).
Can you provide the equational answer to the general problem (arbitrary p of boys)?

Does the ratio remain identical?
Yes

How does the ratio change in the killing case?
Try with a limit of two children per family.
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AxiomOfChoice
Joined: Sep 12, 2012
• Posts: 5761
May 28th, 2014 at 1:44:21 PM permalink
Quote: AceTwo

Not exactly 2 (I thing because we stop at 10)

Yes, exactly, because we stop at 10. I specifically mentioned that I was solving a modified problem where we do not stop at 10, because it makes the problem much simpler (and I can solve it in my head instead of needing paper)

These problems are all essentially the same. You just add up expectations. They are beyond simple. I don't understand why people feel the need to make them difficult. It's like baccarat system players trying to use the fact that they change their betting conditionally to try to beat a negative expectation game. Just like Axel pointed out in another thread, they are taking the simplest possible game and making it as complicated as possible, with the same results. That is exactly what is going on here; people are taking the simplest possible problem and making it complicated.

Just add up expectations. That's it. It could not be simpler. If I can solve a problem in 10 seconds in my head using a simple math theorem, why would I go through pages and pages of calculations, just to come to the same solution (unless I make a mistake in the pages and pages of calculations, in which case the solution will be different)
AceTwo
Joined: Mar 13, 2012
• Posts: 359
May 28th, 2014 at 1:46:09 PM permalink
Quote: FleaStiff

Nature often gives a young mother a female because they are easier to take care of and more experienced mothers get males who roam around more and are adventuresome.

Not true to humans.
In the human population the natural ratio of male to female born is 105:100. There is some scientific reason for this relating to the x and y chromosomes.
This is the ratio observed in western societies.
However the world male to female born is 107:100 and this is due to selective abortion of female featus in countries like China, India etc.

But because women live longer on average there are more women than men, the ratio of male to female alive being around 0,97 in the west.
kubikulann
Joined: Jun 28, 2011
• Posts: 905
May 28th, 2014 at 1:50:04 PM permalink
And the ratio M/F in first-born is equal to the general ratio, putting doubt on the idea that mothers first beget daughters.
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AceTwo
Joined: Mar 13, 2012
• Posts: 359
May 28th, 2014 at 2:02:01 PM permalink
Quote: AxiomOfChoice

These problems are all essentially the same. You just add up expectations. They are beyond simple. I don't understand why people feel the need to make them difficult. It's like baccarat system players trying to use the fact that they change their betting conditionally to try to beat a negative expectation game. Just like Axel pointed out in another thread, they are taking the simplest possible game and making it as complicated as possible, with the same results. That is exactly what is going on here; people are taking the simplest possible problem and making it complicated.

You are 100% right. The problem is like playing roulette and say that I would bet black untill it comes out and then stop. The EVs do not change.
For some reason I thought the problem was different and I thought that there was indeed a bias towards male and the ratio would be favouring males.
In my defence I can say, this is late in the hour where I am from and my quite tired.
24Bingo
Joined: Jul 4, 2012
• Posts: 1348
May 28th, 2014 at 4:08:57 PM permalink
Quote: kubikulann

It is not, since most people provide a wrong answer. Maybe I'm not getting the meaning of "obvious"? I thought it meant "evident", "trivial".

;-) "obviously" again?

Your answer is correct for the special case of 50% chance of boys. Yet that assumption was introduced by a later poster, it is not in the original problem. Can you provide the answers for the general case of p : 1-p ?

Well, that's pretty simple, too, except now the "mothers in a line" version is easier to work with than the brute force version.

First case: again, nothing changes but the mothers. The ratio stays the same.

Second case: again, every girl after a boy followed by 10n girls is killed. Let's allow n to be zero this time (probably should have done so the first time, really). We'll say p is the chance of a girl being born. (1-p)*Σp^(10n), this time starting at zero, adds up to (1-p)/(1-p^10) of a girl being killed, so p/(1-p^10) surviving girls for every boy.

(The girls before the first boy are killed differently, but since the expected number of such girls is fixed - at one - for any population size, they vanish in the long run.)
The trick to poker is learning not to beat yourself up for your mistakes too much, and certainly not too little, but just the right amount.
AxiomOfChoice
Joined: Sep 12, 2012
• Posts: 5761
May 28th, 2014 at 4:18:25 PM permalink
Quote: kubikulann

It is not, since most people provide a wrong answer. Maybe I'm not getting the meaning of "obvious"? I thought it meant "evident", "trivial".

;-) "obviously" again?

Obvious to someone who understands math.

Many people think that they can beat roulette or baccarat by varying their bets in certain ways. I would say that it is obvious that they are wrong, even though many people believe it. Go read the craps or baccarat forums for an example of the stuff that many people believe. Then realize that you are making exactly the same mistake that they are in the blackjack thread.
kubikulann
Joined: Jun 28, 2011
• Posts: 905
May 28th, 2014 at 4:22:56 PM permalink
Quote: 24Bingo

First case: again, nothing changes but the mothers. The ratio stays the same.

Second case: again, every girl after a boy followed by 10n girls is killed. Let's allow n to be zero this time (probably should have done so the first time, really). We'll say p is the chance of a girl being born. (1-p)*Óp^(10n), this time starting at zero, adds up to (1-p)/(1-p^10) of a girl being killed, so p/(1-p^10) surviving girls for every boy.

(The girls before the first boy are killed differently, but since the expected number of such girls is fixed - at one - for any population size, they vanish in the long run.)

This is not the correct answer.
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kubikulann
Joined: Jun 28, 2011
• Posts: 905
May 28th, 2014 at 4:24:35 PM permalink
Quote: AxiomOfChoice

Obvious to someone who understands math.

Many people think that they can beat roulette or baccarat by varying their bets in certain ways. I would say that it is obvious that they are wrong, even though many people believe it. Go read the craps or baccarat forums for an example of the stuff that many people believe. Then realize that you are making exactly the same mistake that they are in the blackjack thread.

Stop the harassment please. Your feeling superior does not give you the right to despise other people. Your (supposed) mathematical skills are matched by a lack of social skills.
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AxiomOfChoice
Joined: Sep 12, 2012
• Posts: 5761
May 28th, 2014 at 4:30:55 PM permalink
Quote: kubikulann

Stop the harassment please. Your feeling superior does not give you the right to despise other people. Your (supposed) mathematical skills are matched by a lack of social skills.

You are the one who is posting questions, and then telling people that they are wrong when they give you the right answers, and then editing your posts when you realize that you are wrong.

Mango's initial answer to your question is spot on. The thread should have ended there. You said that there was something wrong with his solution, then edited that out of your post. The rest of this is you trying to figure out what's going on, and trying to make it more difficult than it really is, to save face.