A Puzzle About Births

I came across this nice puzzle:

In a faraway land long ago, boys were valued more than girls. So couples kept having babies until they had a boy. What is the ratio of girls to boys in this strange land? Assume that the birth of a boy and a girl is equally likely.

Trying to solve this intuitively can be a bit slippery. It somehow gives the illusion that the number of boys would be more than the number of girls. After much intuitive thinking I decided to take on it using probabilities.  I solved it without taking the assumption into consideration, since Lapace’s study of birth ratios has shown this to be false.

Screen Shot 2017-04-16 at 1.48.37 PM.png

Screen Shot 2017-04-16 at 1.50.03 PM.png

So, if we think that the birth of a boy and a girl is equally probable, the ratio of girls to boys  in this strange land(not very strange though, since it still occurs in some places!) comes to be 1. Quite deceptive!

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