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?