During meiosis half of each parent's DNA is lost to the following generation through the process of recombination. Some ancestral ethnicities may well be completely absent if they are a minor component of the parent's DNA. If an ethnicity constitutes more than half of either parent's DNA it will still occur in the child's, even in the most extreme case.
|Sib 1||Sib 2||Sib 3|
|British & Irish||55.7||45.1||42.7|
|French & German||3.1||2.4||8.8|
|Broadly NW Europe||13.3||24.0||15.0|
|Broadly S Europe||4.5||2.3||2.5|
For some insight into how this works use the analogy to a deck of cards. Your parent deals out 26 cards to you from their DNA deck of 52.
If all the cards except aces represent European ancestry the parent has 92.3 percent European ancestry. The 26 cards dealt could contain 0, 1, 2, 3 or 4 aces. Zero aces, means ((26-0)/26) = 100 percent European. 4 aces means ((26-4)/26) = 84.6 percent European. It can't go lower. You could have a greater percentage than your parent.
If the red cards represent British and Irish (B&I) ancestry, and the black any other, the parent has 50 percent B&I ancestry. Dealing out 26 cards it's possible they could all be red (100 percent B&I) or all black, but neither is likely. Using the Hypergeometric Calculator most (90 percent) of the time the percent B&I will be between 35 and 62 percent.
If one suit, say hearts, represents Ashkenazi ancestry out of a deal of 26 cards a maximum of 13 and minimum of zero could be hearts (Ashkenazi). The Hypergeometric Calculator shows that most (90 percent) of the time the percent Ashkenazi will be between 11 and 35 percent. In case you're wondering, the three values for Ashkenazi in the table are well within range for the expected value of 20 percent.
Finally, take the case of one card out of 52 which represents a trace ethnic ancestry. In the deal of 26 cards half of the time that card is absent, zero percent, the other half it's present. That's 3.8 percent, a larger percentage than the parent.
While the analogy with cards is helpful it can be pushed too far. We may or may not inherit an entire parental ethnic segment -- it's as if we could tear the cards in pieces.
Looking further back, at the 10th generation only about half your genealogical ancestors are genetic ancestors, see https://gcbias.org/2013/11/04/how-much-of-your-genome-do-you-inherit-from-a-particular-ancestor/. Cousin marriages amplify the contribution from their ancestry.
If you want to go back even further, contemplate this blog post from John Grenham.