Surnames and illegitimacy - is my math correct?

[Kiltpin]

There are 2 things getting conflated here, and they really should be separated. 

1 - There is the 5%. Out of 100 ancestors, 5 will be illegitimate. I do not know where this percentage came from, but it seems to be accepted as true.

2 - The chances of illegitimacy occurring. Has nothing at all to do with the 5% rate. Believing that it does is how the casinos make their profit. When dealing with chance, particularly human events, the variables are infinite. I believe that the closest we could come to a percentage is 50%. That is to say that the chances are 50/50 in every relationship that illegitimacy will occur. 

Regards 

Chas

[Joby86]

That is what I couldn't understand regarding the illegitimacy rate being a factor when it comes to surnames over generations, I think it would only complicate the thought process lol

[JMB1943]

2 - The chances of illegitimacy occurring. Has nothing at all to do with the 5% rate. Believing that it does is how the casinos make their profit. When dealing with chance, particularly human events, the variables are infinite. I believe that the closest we could come to a percentage is 50%. That is to say that the chances are 50/50 in every relationship that illegitimacy will occur. 
Regards  Chas[/quote]

Let's call a pregnancy resulting from interaction of the woman with ONLY her partner "Faithful".
Similarly, a pregnancy resulting from interaction of the woman with an extra man is "Unfaithful".

For any ONE pregnancy, THEORETICALLY it is either Faithful or Unfaithful, so there are only two possible states, and one of them is Unfaithful; so the probability of the Unfaithful pregnancy is,
1/2 x 100 = 50%, as you say above.

However, the probability that one-half of all women (total number = N) that give birth as "Unfaithful" is NOT 50/50.
It is (1/2) to the (N/2)th power, i.e., for N = 10 women it is 1 in 64, i.e. 1.56%.

Regards,
JMB

[Erato]

"For any ONE pregnancy, THEORETICALLY it is either Faithful or Unfaithful, so there are only two possible states, and one of them is Unfaithful; so the probability of the Unfaithful pregnancy is,
1/2 x 100 = 50%, as you say above."

Hogwash.  Just because there are only two possible outcomes [faithful or unfaithful] doesn't mean that they are both equally likely.  When you buy a lottery ticket, there are only two possibilities - it's a winner or it isn't.  That doesn't mean you have a 50% of winning, though.

[Andrew Tarr]

"For any ONE pregnancy, THEORETICALLY it is either Faithful or Unfaithful, so there are only two possible states, and one of them is Unfaithful; so the probability of the Unfaithful pregnancy is,
1/2 x 100 = 50%, as you say above."

Hogwash.  Just because there are only two possible outcomes [faithful or unfaithful] doesn't mean that they are both equally likely.  When you buy a lottery ticket, there are only two possibilities - it's a winner or it isn't.  That doesn't mean you have a 50% of winning, though.

Sounds as if someone is comparing this with the spin on an electron (50:50), an entirely different situation 

[andrewalston]

Just looking at the maths:

Assuming that the rate of illegitimate births is 5% among both married and unmarried women, and has stayed constant over the period. This is the only statistic we are given.

That means the probability of any individual being legitimate is 0.95.

Over 10 generations, the chances of ALL of the line being legitimate would be 0.95¹⁰, or 0.5987 - call it 60%.

Of course, the illegitimacy rate for births to unmarried women is 100%, which spoils things quite a bit. Traditional written records will usually make these events obvious, while we are still clueless about the proportion of NPEs!

[coombs]

The amount of secretly illegitimate children, born to a man who was not the mother's husband is about 1 to 2%. So one out of 50 ancestors is probably not a blood ancestor, someone else was. But the openly illegitimate percentage is about 5%. So I say about 6 to 7% of all births were illegitimate, including the open NPE's and the secret NPE's.

One of my 4xgreat grandfathers was illegitimate, and one of my 5xgreat grandmothers was illegitimate, no father listed on baptisms.

[andrewalston]

Three of my great great grandmothers were illegitimate - no father named on birth or baptism. That's 18.75%.

However one had her father named on her marriage. The father had left the area soon after the birth if not before, and luckily had an unusual name so I was able to trace him.

Another was from a village where everyone seems to be related to everyone else, so DNA is very unlikely to narrow down a suspect.

The numbers of Bastardy Bonds in the archives hints at a higher illegitimacy rate in the late 18th and early 19th centuries. It was such a common thing that the courts had preprinted forms, with a variant of the form for those cases where the putative father did not show up in court. Some fathers did of course go on to marry the mothers, possibly because it was the cheaper option!

My own paternal line is "officially" documented, mostly in church records, all the way back to my 6xg gf in 1715 - "Abrahamus illegitim filius Patientis Halsted & Abrahami Kersaw amborum Waterside". Patience then went on to marry a different chap called Abraham.