Hmmm…

Assuming it’s actually possible to separate Welsh DNA from Scottish or English DNA – not to mention Irish DNA – then … it’s hard to be sure.

The difficulty lies largely in determining the number of other nations – sovereign, non-sovereign, dependency, federation, territory (disputed or not). The usual figure of 193 regards the UK as one country, not 4. There’s a second figure of 250, which includes dependencies, but that still considers the UK as a single country, not 4.

So I’ll go with 300, which I freely agree is an under-estimate. Wales being one of the 300, if we subtract that we’re left with 299 other countries. Scotland is one option amongst that 299. The probability that the remaining 52% of your heritage is Scottish is therefore

p(Scottish)=1/(300–1), or 0.003.

You’re welcome!