Is it possible to find out my mothers ethnicity if she does not know her biological father?

Question

she knows her mother but noone from her fathers side.

Answer 1

Y-DNA tests determine paternal ancestry within certain broad racial groups--African, Native American, European, and Asian--estimating percentages of each of the racial subtypes.   Nevetheless, at present, these tests can't determine ethnicity beyond a fairly broad category, although testing will break down an individual lineage into percentages of Northern European, Mediterranean, Middle Eastern, and South and East Asian ancestry.  For example, genetically, for now, it's almost impossible to tell English from  Irish,  Austrian from German, and Korean from Japanese--much to all of the above's displeasure.  

Thus, it would be possible to tell if your mother's dad, for instance, was Asian, European, African, Middle Eastern, or more specifically, if he was of Eastern or Southern Asian or of Mediterrean, Middle Eastern, or Northern European descent,  but testing wouldn't reveal his particular nationality within this category.  Similarly, Y-DNA testing would reveal if your dad had any Native American ancestry, but it wouldn't determine to which particular tribe your paternal ancestors belonged.

Mitochondrial DNA tests determine maternal lineage, matching one of the seven daughters of a prehistorical woman called the Mitochondrial Eve.  

Finally, X-DNA tests help determine family relationships in recent generations and/or help reconstruct a family tree.

Google Y-DNA testing and see if you want to pay the fee to determine your mother's dad's ethnic identity within a very broad category.  Looking in the mirror and questioning older family members, however, can perhaps obtain the same results.   Good luck!

Answer 2

She could take a DNA test for ancestry. But that would lump both the father and mother together.