Tracing and quantifying inheritance over many generations
Since it seems my comment helped, I've been suggested to post this as an answer...
I'd reccomend everyone interested in these sort of population genetics to have a look at 'The Ancestors Tale' by Richard Dawkins. In particular, chapter 0, which deals with human/hominid genetics. That should help answer questions. The relevant part of the book appears to be available online for free in GoogleBooks (https://books.google.co.uk/books/about/The_Ancestor_s_Tale.html?id=s86_CQAAQBAJ).
Below I'll note down the answers from the comments section, not because I wrote them but I figured it might help anyone who stumbled over this question afterwards:

The chances of being a direct descendant of 1 individual of the original 10,000 is 100%, assuming they have any descendants. - Tom Melly

If one had a DNA sample of that individual, one could use uniparental markers (either Y chromosome for men, or mtDNA for women) to infer whether they are a direct descendant. - 4galaxy7


(My guess is that it doesn't have to be uniparental markers. Other genes might work just as well. I'm thinking of Neanderthal/Denisovan work. But I might be wrong.)