Steven Landsburg is a brilliant economist and popularizer of economics. His blog –The Big Questions– is always instructive and delightful. I recommend his books meant for the non-specialist enthusiastically. Here he explains why he started writing them.
Begin quote:
One day in 1991, I walked into a medium sized bookstore and counted over 80 titles on quantum physics and the history of the Universe. A few shelves over I found Richard Dawkins’s bestseller The Selfish Gene along with dozens of others explaining Darwinan evolution and the genetic code.
In the best of these books, I discovered natural wonders, confronted mysteries, learned new ways of thinking, and felt I had shared in a great intellectual adventure, founded on ideas that are dazzling in their scope and their simplicity.
Economics, too, is a great intellectual adventure, but I could find, in 1991, not a single book that proposed to share that adventure with the general public. There was nothing that revealed the economist’s unique way of thinking, using a few simple ideas to illuminate the whole range of human behavior, shake up our preconceptions, and jolt us into new ways of seeing the world.
End quote.
To me, economics provides keys to unlock some of the mysteries of the world. I find the world endlessly fascinating. The puzzles I ponder don’t have to be deep or too complex; I am content with small puzzles too. Not just the answers to puzzles, I like to know the various methods that can be used to solve them.
Here’s a simple question that I have known for years. Later I found that Landsburg had discussed it on his blog in a Dec 2010 post titled “Are you smarter than Google?” It begins:
There’s a certain country where everybody wants to have a son. Therefore each couple keeps having children until they have a boy; then they stop. What fraction of the population is female?
I interpret that question to mean “what fraction of the population of children are females.” Anyway, he goes on to write–
I first heard this problem decades ago, and so, perhaps, did you. It comes up in job interviews at places like Google. The answer they expect is simple, definitive and wrong.
That post gets 130+ comments and he follows up with other posts that end up getting over 800 comments.
My answer to that puzzle is simple: the expectation of the fraction of female children is 1/2. That definitive and simple answer, Landsburg claims, is wrong. I think Landsburg is wrong. He’s not a stupid person but he is wrong.
What do you think?
Let’s listen to a song.
Be well, do good work, and keep in touch.
Atanu Dey : Life is a Random Draw 
I have thought about this question quite a few times since childhood. But never went rigorously forward to find a solution. My lazy thinking was that number of girls will be higher in ‘children’ population.
You did a great thing by modifying the question to mean ‘children’ population only. It takes ambiguity away. I am thinking there are N-couples. They will procreate and we are trying to find the distribution within the offsprings ONLY. And that too in first-generation only. The problem still remains puzzling.
Now that I try to solve it, I am thinking it will be 50-50. Let us assume 128 couples (power of 2 helps to calculate). First child will be 64 boys and 64 girls. The couples with girl children will procreate again leading to 32 boys and 32 girls. So after 2nd child in entire community, number of boys and girls will be 64+32 and 64+32. This will continue and distribution will be 50-50.
LikeLike