Geneology statistical probability question?

Question

If according to jewish law, if you have a jewish mother, then ethnically you are a jew, whether you practice it, or know it or not (maternal lineage). If you go back 20 generations (600 years ago, if you assume 30 years a generation) you have 1,048,576 ancestors in that 20th generation. If 10% of those ancestors are jewish, what are the odds of you being a jew? How about if 1% of the ancestors are jewish? You have to take in acount that as long as the maternal line is not broken, all the female ancestors are jewish whether they know it or not. And if the maternal line is broken, it can be restarted again by any male ancestor marrying a female jew. I am not sure how many children the average couple has on this planet, so lets assume for arguments sake the average couple on this planet has 4 children. Can this be statistically calculated?

Answer 1

Interesting...

Let's say 10% of the people in a generation are Jewish. I assume this is equal for males and females,so 10% of the couples have a Jewish mother, and produce Jewish children. The remaining 90% will produce goyim. So the next generation will again have 10% of Jewish people.

Since the 10% proportion doesn't change from one generation to the next, your odds of being Jewish are 10%. That's assuming Jews have as many children as non-Jews.

Answer 2

I don't know about genetically composite but all I know is about generations... 7th generations down the line and you'll still be called a relative . So, any seventh cousin of a Jew... would still be a Jew, I presume.