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 Jun 5 awarded Yearling Nov 29 awarded Nice Answer Nov 10 awarded Nice Answer Sep 24 awarded Autobiographer Jun 23 awarded Nice Answer Jun 5 awarded Yearling Jan 12 awarded Popular Question Sep 24 awarded Nice Answer Aug 11 awarded Nice Answer Aug 5 awarded Nice Answer Jun 25 awarded Pundit Jun 5 awarded Yearling Nov 19 awarded Good Answer Jun 5 awarded Yearling Jan 14 awarded Necromancer Jun 6 awarded Yearling Apr 16 awarded Nice Answer Feb 26 awarded Good Answer Jan 4 comment Google question: In a country in which people only want boys I'm not assuming any specific model, but pointing out that differences between your answer and 1/2 arise from artificial (i.e., gender-asymmetric) conditioning of the problem. Assuming $k$ families as in Zare's model or your present suggestion, is equivalent to assuming "at most $k$ boys in population", or exactly $k$ boys if it is also assumed the families complete their reproduction. No such asymmetric conditioning was part of the Google problem. Your calculations show that a symmetrical distribution can be approximated by asymmetric ones, not that the Google problem is asymmetric. Jan 4 comment Google question: In a country in which people only want boys Steven, that is incorrect. The issue is whether the proportion of boys, denoted $f(B,G)$ above, is convex as a function of two variables so that $E[f(B,G)] > f(E[B],E[G]) = 1/2$. It isn't convex, as simple calculations demonstrate. (See the comments on convexity and Jensen's inequality under Douglas Zare's posting). It is convex if you condition on B (i.e., restrict f to lines B=constant), and concave if you condition on G. Such conditioning is foreign to the Google problem and imposed artificially in Doug's model.