Girl Named Florida

As I mentioned in the previous post, by adding the condition that a family with two children has a girl named Florida the odds go from 1:3 to 1:2 that the other child is a girl.

Florida was one of the top 1000 female names between about 1900-1930 according to Mlodinow and the Social Security office. But now let’s say it’s a 1:1,000,000 name for girls. The possibilities for families include (assuming they won’t have two girls named Florida): (b,b), (b,n), (b,F), (n,b),(n,F), (n,n), (F,b), (F,n), where b=boy, n=girl not named Florida, F=girl named Florida.

Since we know the family has a girl named Florida we can throw out (b,b), (b,n), (n,b), and (n,n). That means there are 4 ways to have two children families with a girl named Florida, (b,F), (n,F), (F,b), and (F,n), two ways with boys and two ways without.

For more nuanced analysis of this problem check out:
There once was a girl named Florida (a.k.a Evil problems in probability)
Two-Child Paradox Reborn?

Odds of a Girl

I read great new book called The Drunkard’s Walk which is essentially about how the random effects our lives more than we imagine. He had a number of interesting examples of how to think in these terms, all pointing to the importance of asking the right questions and thinking about how to answer it right ways.

For instance if you ask, “A family has two children, one of which is a girl. What are the chances the other one is too?” The answer is 1:3. That’s because we know there are the following combinations possible in birth order: (girl, boy), (girl, girl), and (boy, girl). The (boy, boy) combination is ruled out by what was said about the family. So three equal possibilities, odds are 1:3 that the family would be (girl, girl).

Ah but what if one of the children were named Florida? What then of the odds? It turns out to be 1:2. I’ll show you how in my next post.