No, the sampling does not work like that, that way lies madness (or poor results). The models oversample the most likely options and undersample rare options. A

No, the sampling does not work like that, that way lies madness (or poor results). The models oversample the most likely options and undersample rare options. Always picking the most likely option leads to bad outcomes, and literally sampling from the actual probability distribution of the next word also leads to bad outcomes, so you want something in the middle and for that tradeoff there's a configurable "temperature" parameter, or in some cases "top-p" parameter where sampling is done only from a few of the most likely options, and rare options have 0 chance to be selected. Of course that parameter doesn't only influence the coherency of text (for which it is optimized) but also the facts it outputs; so it should not (and does not) always "pick the most likely family", but it would be biased towards common families (picking them even more commonly than they are) and biased against rare families (picking them even more rarely than they are). But if you want it to generate a more varied population, that's not a problem, the temperature should be trivial to tweak.