Why is it impossible? It's certainly possible to tell apart cat and dog DNA. If the race theory proponents argument hold water, the same must be possible for different races.
Here is a link to the Kahn Academy course on statistics: https://www.khanacademy.org/math/statistics-probability
If you take this course, you will understand probability better, and then you wont commit the logical fallacy of "false dichotemy" where you try to reduce complexity to binary classes which is a view that is too simplistic to accuratly represent the distributions we are talking about
That image does not contain 'race', and it comes from a paper that does not even mention the word 'race'. You have provided no arguments that race exists. The paper writes:
> This observation ... will make it a challenge to trace the ancestry of African Americans to specific ethnic groups in Africa, unless considerably more markers are used.
The more markers you use, the more different groups you get. You can of course choose to 'cluster' them, but then some precision will be lost, and what exactly will be gained?
