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Maths vs the Chinese government

27 Aug 09 | Re: Weird one-child quirk (or actually not)

Most people know about China’s one-child policy: in order to curb population growth, couples are only allowed to have one child. Most people also know that in rural areas, families who don’t have a son are allowed to have more children in the hope of having a son to help out with agricultural work.

I don’t know the actual detail of this exception, but let’s assume that:

• couples are allowed to keep having children until they have a son, and then have to stop
• every child a couple has is equally likely to be a son or a daughter, regardless of what they have had previously
• everyone sticks to the rules, and everyone is able to keep having children until they eventually get a son.

Based on these assumptions, in a sample of 1024 couples:

• 512 will have a son
• 256 will have a daughter and then a son
• 128 will have two daughters and then a son
• 64 will have three daughters and then a son
• 32 will have four daughters and then a son
• 16 will have five daughters and then a son
• 8 will have six daughters and then a son
• 4 will have seven daughters and then a son
• 2 will have eight daughters and then a son
• 1 will have more than eight, let’s say nine, daughters and then a son.

That gives us a total of 1024 sons and 256 + 256 + 192 + 128 + 80 + 48 + 28 + 16 + 9 = 1013 daughters.

Hmm. I was thinking before I just worked that out that it would lead to way more girls, even though it was designed to make sure there were enough boys, but it’s actually equal. Score one for the Chinese government I suppose. Good policy.

Update: See next post for more things that are wrong with the above.

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