Imagine for example there were just 1 boy-girl family, and they produced offspring until they got a boy and then stopped.Then the proportion #boys/#girls is 2/1 with probability 1/2, 2/2 with probability 1/4, 2/3 with probability 1/8,...For help making this question more broadly applicable, visit the help center.
I just wanted to say, that you assume that all children of one family are born instantaneous (with the last child a boy).
If you take into account "unfinished" families, than the proportion is directly 50/50 (I think, because how matter what, the change of boy for a child is 50/50)[email protected] Landsburg: There were some very interesting and thoughtful comments on your post. I was told it by Vin de Silva, who said he was told it by Imre Leader, but I have no idea what the original source is.
Starting to solve the problem for myself I got that part of girls can be calculated with following series: $$\sum_^\frac\left (1-\frac\right )$$ This leads to an answer: there will be ~61% of girls.
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All we know is that in $k$ families, some number $n$ of births have occurred through time $t$, each birth equivalent to a fair coin toss.