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Baby Ratio Puzzle - Solution
The Puzzle:
In Girlia a family is not considered complete until a girl is born.
So every family continues to have children until they have a girl.
What would the ratio of boys to girls be there?
(Assume that having a girl or boy is equally likely.)
Our Solution:
Let's say you have 1000 families.
After each family has their first child there will be about 500 girls and 500 boys.
The 500 with girls will stop, and the current boy:girl ratio is 1:1.
The 500 families with boys will have another child: about 250 will be boys and 250 girls.
The 250 that had girls will stop, and the current boy:girl ratio is still 1:1.
The 250 that now have two boys will have another child, about 125 new boys and 125 new girls. The ratio is still 1:1, wow.
This continues on!
The ratio stays the same at 1:1, not what you may have expected.
In fact the probability of having a boy or girl is independent of any previous children.
After each family has their first child there will be about 500 girls and 500 boys.
The 500 with girls will stop, and the current boy:girl ratio is 1:1.
The 500 families with boys will have another child: about 250 will be boys and 250 girls.
The 250 that had girls will stop, and the current boy:girl ratio is still 1:1.
The 250 that now have two boys will have another child, about 125 new boys and 125 new girls. The ratio is still 1:1, wow.
This continues on!
The ratio stays the same at 1:1, not what you may have expected.
In fact the probability of having a boy or girl is independent of any previous children.