text: This is what's known as a Fermi question. You have to make certain assumptions and guesses, and use them to come up with a possible answer. Here's an example of how to do this problem.\n\nFirst of all, there are 973 years between 1027 and 2000.\n\nWhat's the average net population growth rate for a human population? Let's say it's 1.6% per year over these 973 years - because it's proportional to itself we'll be using an exponential growth equation. Starting with 1 (William himself), we can go 1*(e^(0.016*973)) the population borne out of William the Conquerer will be about 5.7 million. That sounds huge but we're talking about a millennium here, and most of them will have long forgotten about their ancestry (cause of all the daughters.) However, that 5.7 million will be the number of people alive. We're just looking for the population aged 0-1. In 2002 about 10% of the world was aged 0-4 and assuming similar characteristics for 2000 and even distribution inside 0-4 for each year, about 142,500 Conquerer kids were born in 2000.\n\nHow many people were born in the year 2000? Assuming 350,000 births a day over 366 days (leap year), 128.1 million people were born in the year 2000.\n\n142500/128100000 = 0.11%\n\nThat means the odds are about 1 in 900. Better than you'd think? Again, this could be widely varied depending on the assumptions you make. But I think that might be in the ballpark.