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?
A good analogy for this is flipping a coin. What is the proportion of total heads to total tails if a population of people each flip a coin until they get a heads. The answer is fairly trivial, as each coin flip is independent. Given a fair coin, you would expect the answer to be near 1. You could always calculate the variance given the population size using the binomial distribution.
A more fruitful question might be: what is the average family size in a country with these birthing habits?
If we assume there's an even chance of having a boy or girl, the proportion of boys to girls is still 50/50. It's basic stats. These are independent events.
