Puzzle
In a country in which people only want boys, every family continues to have children until they have a boy. If they have a girl, they have another child. If they have a boy, they stop. What is the proportion of boys to girls in the country?
My solution (not finished)
If we assume that the probability of having a girl is 50%, the set of possible cases are:
Boy (50%)
Girl, Boy (25%)
Girl, Girl, Boy (12.5%)
…
So, if we call G the number of girls that a family had and B the number of boys that a family had, we have:
$B = 1$
$P(G = x) = (1/2)^{x+1}*x$
So
$G = \Sigma (1/2)^{x+1}*x$
I feel like the sum of this infinite serie is 1 and that the proportion of girls/boys in this country will be 50%, but I don't know how to prove it!
Thanks!
Best Answer
This is a trick question!
This question is very simple if you just learn to accept that most of the information given is completely irrelevant...
It doesnt matter how many families continue to have children and how many stop at 1 or 2...its no more relevant than what car they drive...
None of the information provided alters the statistical probability of a child born being male or female...its still 50%