Maths interview question: gender-ratio

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This is apparently a common interview question:

In a bid to have more boys, every family in a certain country will continue to try for children until they have a boy. If they have a girl, they’ll keep trying. If they have one boy, they’ll stop. What will be the proportion of girls to boys in this country?

The answer is 50:50.

Imagine there are 100 couples have their first child. 50 will be girls, 50 will be boys.

The 50 that have girls will try again. Of these, 25 will be girls, 25 will be boys. So the number is now 75 girls to 75 boys.

Of the 25 that had girls will try again. Of these, 12.5 will be girls, 12.5 will be boys. So the number is now 87.5 girls to 87.5 boys.

And so on. The ratio will always be 1:1.