TITLE: Google question: In a country in which people only want boys
QUESTION [95 upvotes]: Hi all!
Google published recently questions that are asked to candidates on interviews. One of them caused very very hot debates in our company and we're unsure where the truth is. The question is:

In a country in which people only want
  boys every family continues to have
  children until they have a boy. If
  they have a girl, they have another
  child. If they have a boy, they stop.
  What is the proportion of boys to
  girls in the country?

Despite that the official answer is 50/50 I feel that something wrong with it. Starting to solve the problem for myself I got that part of girls can be calculated with following series:
$$\sum_{n=1}^{\infty}\frac{1}{2^n}\left (1-\frac{1}{n+1}\right )$$
This leads to an answer: there will be ~61% of girls.
The official solution is:

This one caused quite the debate, but
  we figured it out following these
  steps:

Imagine you have 10 couples who have 10 babies. 5 will be girls. 5
  will be boys. (Total babies made: 10,
  with 5 boys and 5 girls)
The 5 couples who had girls will have 5 babies. Half (2.5) will be
  girls. Half (2.5) will be boys. Add
  2.5 boys to the 5 already born and 2.5 girls to the 5 already born. (Total
  babies made: 15, with 7.5 boys and 7.5
  girls.)
The 2.5 couples that had girls will have 2.5 babies. Half (1.25) will
  be boys and half (1.25) will be girls.
  Add 1.25 boys to the 7.5 boys already
  born and 1.25 girls to the 7.5 already
  born. (Total babies: 17.5 with 8.75
  boys and 8.75 girls).
And so on, maintianing a 50/50 population.


Where the truth is?

REPLY [4 votes]: Caveat: This is not an entirely serious answer.
There has been some (heated?) discussion as to the sensitivity of the various answer to the particular model. I thought, for my own amusement, that I would
do some Monte-Carlo experiments with a "plausible" model involving Pilgrims
traveling to the New World. However, in thinking about possible models, I came up with the following issue.
Suppose we assume that:

Once Pilgrims marry, they stay married, and do not re-marry if their spouse dies.
No living Pilgrim has a direct living ancestor older than their grandparents.

Under these assumptions, it follows that if there were N male Pilgrims in the first settlement, then, at any given time, there are at most 3N male Pilgrims. Moreover, the probability of the settlement dying out over several generations (because all the children are girls) is non-zero. By Kolmogorov's zero-one law (overkill), it follows that almost surely the Settlement will die out, and not become the kick-ass country it may well have been.