[thaumasiotes]

> You are correct in the zero sum outcome for the //ENTIRE// homeless population; however you are not correct in the sense of a hypothetical subject being homeless.

This is wrong. What's correct as a description of the entire female homeless population is equally correct as a probability assignment for one element of it.

Your second sentence is unrelated to your first, and also applies equally well to the entire population as to an individual sample from it. It is arguing that the sum I describe is in fact more than 1. That is defensible, but it won't make the statements independent; they aren't.