What are the chances of having autosomal DNA from an ancestor N generations back?

I understand that everyone carries autosomal DNA from both their mother and their father. Because there are only a small number of crossovers per chromosome, I see that not everyone would carry any DNA from an ancestor several generations back.

What are the chances of a person carrying any DNA from an ancestor N generations back, where N > 1 and the simplifying assumption is made that no ancestor appears more than once?

This is exactly the question I answered in my blog post about 2 years ago: Probability of No Autosomal Segments Matching

The final table of probabilities I came up with was:

• The chance of a person carrying any DNA from an ancestor 5 generations back is 99.78%
• The chance of a person carrying any DNA from an ancestor 10 generations back is 29.86%
• The chance of a person carrying any DNA from an ancestor 15 generations back is 1.61%
• etc.

The probability curve of no segments matching (which is 100% minus the chance that a descendant carries DNA) looks like this:

Here are a couple resources for you:

Concepts – Percentage of Ancestors’ DNA

This chart provides a summary of how many ancestors you have in each generation, an approximate year they were born using a 25 year generation and a 30 year generation, respectively, and how much of their DNA, on average, you could expect to carry, today. You’ll notice that by the time you’re in the 7th generation, you can be expected, on average, to carry 0.78% meaning less than 1% of that GGGGG-grandparent’s DNA.

How much of your genome do you inherit from a particular ancestor?