Well let's ignore the fact that Mongolia, Russia, and Ethiopia are places, not races. The underlying issue is:
Race is a social term used to generalize the ancestry of a person. It's to vague to make a prediction about the genes, and their expression, in a particular person.
There is a lot of genetic diversity even in, what can be considered, a genetically homogeneous population. Genes that have been unexpressed for generations can suddenly appear again if the right couple have offspring. Even the genetic expression within offspring from a single couple can vary wildly. I think most of know cases similar to the family with 3 brown hair and eyed kids, and 1 with blonde hair and blue eyes.
You throw genetic diversification increases from a few 100 years of globalization into the mix and the whole notion of scientifically defining a race, let alone predicting actual gene expressions in a individual, becomes ridiculous.
Predictions of gene expression can only be done on a case by case basis within a specific heredity context. This is the reason the doctor's form asks for your parent's, grandparent's, and siblings medical history, not what race you are.