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I've just read that if a person has 27% Native American DNA on their father side, that means their father is at least 27% Native American and at most 77%, and their grandparent is at least 77% Native American and at most 100%. Does that mean that there is a possibility that a person who is 1/2 Native American and European might get 100% Native American DNA if they had their DNA tested?

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No, a person half Native American (NA) and half European would not show as 100% NA on a 23andMe test. They should show no more than 50% NA on the test, and might show less, like 40% or 45% NA with 5 or 10% of "NA or East Asian" or "unknown" (with the other 50% showing up mostly as some form of European, maybe with a bit of "unknown").

I don't see how your ultimate question related to your preliminary example. In that example, the characterization of the father was okay, but that of the grandparent(s) wasn't. The father would have to have been 27% to 77% NA (and most likely around 50%), although only if the mother was known to have 0% NA.

The father could have gotten his NA and his European from either or both of his parents. If the NA was from both of them, they could each have had as little as 27% NA (if all of that went to the father; not very likely). If only one of the father's parents had any NA, then that parent could have had 100% NA, but could also have had down to as little as 54% NA (but no less).

The most likely scenario for a person of 27% NA with a mother of 0% NA, would be a father with about 50% NA and his parents with about half of their combined DNA being NA, which could have been distributed in many ways, from 50% NA each to 100% NA in one parent and 0% NA in the other.

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