In The Drunkard’s Walk, Leonard Mlodinow presents “The Girl Named Florida Problem”:
“In a family with two children, what are the chances, if [at least] one of the children is a girl named Florida, that both children are girls?”
I added “at least” to Mlodinow’s statement of the problem to avoid a subtle ambiguity.
I wrote about this problem in a previous article from 2011. As you can see in the comments, my explanation was not met with universal acclaim.
This time, I want to take a different approach.
First, to avoid some real-world complications, let’s assume that this question takes place in an imaginary city called Statesville where:
- Every family has two children.
- 50% of children are male and 50% are female.
- All children are named after U.S. states, and all state names are chosen with equal probability.
- Genders and names within each family are chosen independently.
Second, rather than solve it mathematically, I’ll demonstrate it computationally:
Either way, I hope you enjoy getting your head around this problem.