A good discussion on today's edition of "More or Less" (Radio 4, now available on iPlayer Radio), regarding the statistical probability of being descended from Edward III.
If you have UK ancestry, the chances are heavily in favour of you having him as a direct ancestor.
I still do not understand how it is possible

.
For this to be true, his children and their descendants would have had to have had a lot of marriage/relations with commoners.
The approx population of the UK in the 14th century was 3.5 million, the majority of people would have been some kind of agricultural labourer.
How likely is it that over the centuries the aristocracy married into, or even met in person, the peasantry?
The "statistics" do not seem to take into account that people married within their own social class and did so for many centuries