It is been commonly reported by the media that India’s skewed gender ratio—roughly 950 girls to 1000 boys—is caused by the “stopping rule” (families having children until a son is born, then stopping).
This results in a 1-child family will always be a son, and a 4-child family will have three daughters and a son. Then will there be more sons or more daughters?
Thought Experiment
Imagine 1,000 couples who only stop once they have a boy.
- Round 1: 1,000 babies are born.
- Statistically: 500 Boys, 500 Girls.
- The 500 parents of boys stop.
- The 500 parents of girls try again.
- Round 2: 500 babies are born.
- Statistically: 250 Boys, 250 Girls.
- The 250 parents of boys stop.
- The 250 parents of girls try again.
- Round 3: 250 babies are born.
- Statistically: 125 Boys, 125 Girls.
No matter how many rounds you play, the number of boys born in each round always equals the number of girls.
Independent Event Principle
The math holds because each birth is an independent event. Nature has no memory; the probability of a boy or girl is always 0.5 for every single birth, regardless of what came before.
“stopping rule” decides the number of births, but it cannot change the probability of those births.
Conclusion
Mathematically, if you let nature take its course, “stopping after a boy” will always result in a 1:1 ratio. The observed skew in the population is a result of human intervention—where the “coin flip” itself is manipulated—not the statistical outcome of stopping rules.
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