Chinese Baby Puzzle
"Where the ladies at?"
Alright kids, here’s a puzzle to keep your brain active over the weekend.
China has a population problem. Not only are there too many people, there are too many men! This biased ratio is mainly due to cultural traditions regarding male heirs and the unfortunate abortion of female babies. Very sad, and a very real issue.
To help alleviate the problem, the Chinese government imposes some strict rules on couples. You are only allowed to have one child. If your child is male, you may not have anymore children. However in lieu of the abortion problem, if your first child is female, you have the option of having exactly one more child.
With this system in place, (and assuming this eliminates the abortion problem) what will be the ratio of men to women? How many couples must take advantage of this “bonus” child rule for it to help the sex-ratio problem?
First correct answers get a million “Sprocket Points”.
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11:05 AM on November 6th, 2009
If there are no abortions, and we assume that it is random whether or not a couple has a boy or a girl, and that the sex of their second child is independent of the sex of their first child, then it is completely irrelevant how many couples take advantage of the policy to have a second child.
The ratio of men to women born will stay at 50%.
Take a population that is having kids.
They have kids – half boy and half girl
++++++======
If they have a girl, they have another kid – whose chances of being a boy or girl are 50/50
++++++======
+++===
Or maybe only a fraction of them have another kid – again, with the odds of either sex at 50%
++++++======
+=
On average, with no abortions / infanticide, the population will tend to even out to a 50/50 ratio.
Unless I’m missing something?
11:08 AM on November 6th, 2009
Of course, it has been scientifically demonstrated that attractive people tend to have more female children, so the sex of the second child is not completely independent of the sex of the first child – the first child being a female tends to indicate that the parents are more attractive and will tend to have slightly more female children, so even if the ratio is initially 50/50, with this policy, there will tend to be more female children born than males, upsetting that ratio slightly in favor of the females:
++++++======
++++==
7:32 AM on November 9th, 2009
One million points to Nato.
He’s correct: this system actually has no affect on the standard 50-50 sex-ratio. As Nato pointed out, regardless of any system, births will continue to stay 50-50.
In fact, you could modify the problem to say: “You can have as many girls as you want, but once you have your first boy, you must stop having children.” And you’d still have a 50-50 ratio. Somewhat counter intuitive, but true!
Congrats Nato!