Fun math: Chinese baby problem

[JVS]

Answer this question: if the Chinese government forbids parents from having more children after a son is born, is the gender distribution of China's children affected in any way? Please show how you arrived at your answer.

[kick-ass-bob]

1. No.

Because I pulled it out of my ass.

:D

[Debi]

6. You, Bob, are a Jenius! n/t

[nini]

2. yes.. you'll end up with more girls

if the first child is a girl.. you can try again. You may get another girl...etc

if the first child is a boy.. then you're done.


possibility of more girls in the long run

[Cathyclysmic]

3. statistically ...

the population of the world is 51% female, 49% male for various reasons....you'll end up with more girls in the long run.

[XemaSab]

17. weak chromosomes

n/t

[AllegroRondo]

20. but thats not at birth

the world population is 51/49 female to male, but thats mostly due to males having a shorter life span

at birth, its approximately reversed, 51/49 male to female.

go figure.

[Cathyclysmic]

26. yes, so over time , you will have a higher female population...

wasn't that the question?:shrug:

[AllegroRondo]

4. Hmmmmmm

Lets say you only have two families....

Family A has a boy, and must stop.
Family B has a girl, so tries again, and has a boy.

Total so far: 2 boys, 1 girl.


So....

If you have 1,000 families, you end up with 1,000 boys and 500 girls.
extrapolate from there.

[AllegroRondo]

5. But - it gets more difficult after that

lets say theres a 50/50 chance of either sex, just to make it easy


1000 families, after round 1 you have 500 boys and 500 girls

the families that had boys must stop, those with girls can try again.

after round two, the families that could go again have 250 boys and 250 girls
total so far: 750 to 750


round three, the 250 that had girls try again, with 125 boys and 125 girls
total so far: 875 to 875


keep going, you end up with a total of only one more boy than girls.

so while any single family will have at least one boy child, any family with more than one child can only have one boy. so it evens out.

my head hurts. Im getting a beer.

[Bill McBlueState]

8. interesting

It's counterintuitive, but I think you're right.

Even though any one family could have infinitely many girls, the odds of this are vanishingly small. It's a limiting process.

[NewJeffCT]

9. I think you are correct

But, I'm not nearly as good with that thinking stuff as I used to be.

[LynzM]

12. That makes sense statistically....

Now try to figure in the number of children that any family will have, supposing they don't first have a boy... :evilgrin: That's the harder part, methinks!

[AllegroRondo]

19. Lets see.....

if you work with the 1000 family sample from before, the largest family would be 10 children. (2^ n-1)= 512 , approximately half the population with a 50% chance for boy or girl.

a sample of 10,000 families would max out at about 12-13 children for the largest, (2^12 = 4096)

at 100,000 families the largest is 15-16
at 1,000,000 families, the largest is around 19


I need another beer

[nini]

13. makes sense

.




I think :D

[ProfessorGAC]

22. You're Only Sort Of Right

The answer is determined by Bayseian equations. While the effect is small, the answer is that more girls will ultimately be born, by about 0.4%.

The problem with your approach is that you aren't introducing the intersection concepts of set theory to your probability values. Remember, that per your event sequence, the probability of the family having a boy the second time isn't really 50:50, because the probability of having two girls in a row is 1 in 4, not 50:50. Think of it in coin flipping. If you flip 3 heads in a row, you would say that the next flip is 50:50, heads or tails. However, getting 4 heads in a row, is a one in 16 chance.

A Bayes equation will give you the actual values as you go through the iterations in the same way you did, except it will allow for the progressive probability of a series of intersecting 1:1 events to be included.
The Professor

[LynzM]

23. This is the thing about probablility that kills me...

Why can't you consider each event to be its own, new event? As in, each time you have a 50/50 chance? The previous child you had should have no affect on which gender you conceive the second time, right? Same for coin flipping. I mean, I can see:

H/H
H/T
T/H
T/T

gives you only a one in 4 chance of getting two Hs in a row, but if you look only at the second event, it's still 50/50. In other words, given that you've already gotten one H, your chance of another H is still 50/50, no?

*ow, my brain* ;)

[AllegroRondo]

24. Not exactly

the probability of any family having two girls in a row is 1 in 4, but the probability of a family that already had a girl having a second one is 50/50. The families that had a boy first are dropped from the second iteration.

Like the coin toss example, getting 4 head in a row is 1 in 16, but if you already have 3 heads, youre back to 50/50, not one in 16. The coin has no memory of the previous tosses.

[Bill McBlueState]

30. Come back, GAC!

I know from your previous posts that you definitely know what you're talking about when it comes to statistics, but like the other two posters say, the coin doesn't remember what happened on the last flip. Tell us more about this Bayesian stuff!

[ashling]

7. I have no idea

but, did you hear about the right wing neo-Christian redneck woman from Alabama who refused to have more than three children because she heard that every fourth child born was Chinese?

Didn't think so.

[obxhead]

10. Look to the laws of hunting.

It takes a male and female to make an offspring. It also holds true that 1 male and 10 females can create 10 or more offspring.

[JVS]

11. Kick

[GirlinContempt]

14. Yes.

The boys all end up killing eachother off, so, more girls.

[nashbridges]

15. They don't forbid more children after a "son" is born

by practice, you have to apply to have more children after you have "one" (either sex). I lived there for three years between Hong Kong and the Beijing outlying areas, and the effect is to abort female children if you can, and pretend you didn't have them if you do. The Chinese put an emphasis on male family members, and this is an expected response.

Neither solution is a good idea. But on the books, the most common reason for a request to have another child after your first is because your first child was female. This has been policy for 30 years, and it doesn't appear to be swinging the gender statistics of China appreciably. The Chinese people are aborting female pregnancies so they don't have to bother.

However, they did succeed in limiting population growth for the country - if the policy wasn't in place population predictions of 1.3 to 2.2 times the current Chinese population were expected since 1975, which didn't happen.

Most families (remember, it's a country of a billion people or more) keep their first born because of the same reason that most people keep their first born: It's their child! The number of parents who abort and/or apply for another birth license is very small because it is limited to parents trying to trick the system to their benefit, or supposed benefit.

The "one child" policy that most people quote doesn't exist, but it is very hard to have MORE than one child. It sounds ridiculous in America. However, in all fairness, China is not forcing people to abort all of their second children. That's not the law. The law states that you need approval for your second child. Of course, I don't consider that a good policy, either.

[JVS]

16. It's for a math problem, not for a report on real conditions there

[nashbridges]

18. Oh okey dokey,

Get a hold of statistics for birth rates and figure out what sex is favored for first births in China. If most first births are female, then that is your answer. You can continue the research by checking the likelihood of second births being male or female, and find the answer there.

If every first female birth is followed by a male birth, then the policy will make no difference.

If every first male birth is not followed by a female birth, then the only way it will equal out is if female first births are close to male first births.

But it wouldn't seem to matter the way you've stated the problem, since a female birth is allowed as long as a male birth happens later. Everything evens out. In fact, your scenario would appear to favor female births as long as you assume a 50/50 chance of having a baby of a particular sex.

Better?

Just trying to help...

[Commie Pinko Dirtbag]

21. OK, so we have an infinite series

he - 1/2 of families

she, he - 1/4

she, she, he - 1/8

she, she, she, he - 1/16

she, she, she....... he - 1/2^n

Men: sigma(i=1 -> infinite) 1/2^i = 1
Women: sigma(i=1 -> infinite) (i - 1)/2^i = -1 + sigma(i=1 -> infinite) i/2^i

OK, I cheated. I "converged" that last infinite series on a spreadsheet program and found it is equal to 2. Therefore the sex distribution is still the same.

Edit: I found an elegant way of showing that sigma(i=1 -> infinite) i/2^i equals 2. Express x = the sum term to term, then express 2x term to term. Subtract x from 2x, term to term with the same denominator. You fall back to the previous 1/2^i sum, plus one.

[AllegroRondo]

25. thats it

you end up with 50% + 1 boys.

but you expressed it much more simply than I could.

[JVS]

27. I think you have the right answer, but did you consider families...

that quit before having any son?

[Commie Pinko Dirtbag]

28. You're right. The real effect is more girls, then.

[AllegroRondo]

29. I'm not sure

the odds of having a boy or girl havent changed, just the ability to have more kids.