I'm not talking about correlation vs. causation. Considering correlation alone, "most billionaires are male" does not mean that selecting only males will help

I'm not talking about correlation vs. causation. Considering correlation alone, "most billionaires are male" does not mean that selecting only males will help maximize the number of billionaires you pick, especially since billionaires are a small group while males are a large one. Suppose 1% of males are billionaires and 0.1% of females are billionaires. (Then if the total population is half male, this means 89% of billionaires are male.) Eliminating females from your sample will increase your "billionaire rate" from .55% to 1%. Now suppose that 10% of billionaires are children of billionaires; half of those are male and half female. Let's say 1% of both males and females are children of billionaires. Suppose your college has two applicants, a male child of a billionaire, a female child of a billionaire, and a male child of non-billionaires. Which has a better chance of being a billionaire? In this (totally contrived) example, "child of a billionaire" is a better predictor for "billionaire" than "male" is (even though "billionaire" a predictor for "male" than for "child of a billionaire"). The college that wants to maximize billionaire alumni should not select only males. Instead, it should choose children of billionaires over all others. Then the rate increases to 5.5%.