Surnames and illegitimacy - is my math correct?

[RJ_Paton]

I don't think this is correct. Think of it this way......

there is a game in which you have a 5% chance of winning - if you play once, you have a 5% chance to win, but if you are allowed to pay twice, you have a 10% chance you will eventually win, play four times, a 20% chance etc.

No, in the example you give  the probabilities of winning each game remain at 5% regardless of how many times you play - the percentages aren't stacked up in that manner.

[Andrew Tarr]

I don't think this is correct. Think of it this way......  there is a game in which you have a 5% chance of winning - if you play once, you have a 5% chance to win, but if you are allowed to pay twice, you have a 10% chance you will eventually win, play four times, a 20% chance etc.

You'll have to modify your maths a bit, as if you play your game 20 times you are certain to win Overall probabilities are usually rather less simple than you think 

Family history records are always beset by the snag that informants often gave the info that the recorder wanted to hear, and there was usually no way to verify anything, even if needed.

[melba_schmelba]

I don't think this is correct. Think of it this way......

there is a game in which you have a 5% chance of winning - if you play once, you have a 5% chance to win, but if you are allowed to pay twice, you have a 10% chance you will eventually win, play four times, a 20% chance etc.

No, in the example you give  the probabilities of winning each game remain at 5% regardless of how many times you play - the percentages aren't stacked up in that manner.

I am not talking about winning each game , I am talking about eventually winning. And surely the more times you play a game, the more times you throw a dice, the more likely it becomes the more times you do it, that you will eventually win or get the right number .

[melba_schmelba]

Well, I think I have possibility found the correct equation 

https://math.stackexchange.com/questions/1894684/what-is-the-chance-of-rolling-a-specific-number-after-a-certain-amount-of-rolls

 1−(1−1/x)^y

this referring to the probability of getting a 6 on a six sided dice after six rolls

So (I think) using the same logic, thinking of ten generations where there is a probability of 5% that the child will have a father of a different surname

1 - (1-(5/100))¹⁰ = 0.40

i.e. I think the chance in 10 generations that you will have an ancestor in the male line of someone who was born to someone of a different surname is 40%??

[melba_schmelba]

Some more probabilities using the same equation..of an ancestor in the male line having a surname different to their biological father

in 20 generations i.e. approx 600 years = 64%

in 5 generations i.e. approx 150 years = 23%

[Guy Etchells]

If the supposed average rate of illegitimacy is 5% - does that mean, in 10 generations i.e. on average, about 300 years, the likelihood of your ancestor in the male line being someone of a different surname is 50%? And in 600 years, it is almost certain that one of your male ancestors would have had a father who was not who he was meant to be (or they inherited their mother's surname) ?

No, because the statistics do not show that they" show-" Illegitimate births accounted for 4–6 per cent of recorded births between 1860 and 1930 (40,000–65,000 a year).

So for the sake of simplicity round the percentage to 5%.

That is still not an average percentage of births by the married population as it includes many births by single women, in addition it does not take into account how many women have more than one illegitimate child, some have 5 or 6.
In a similar way some married women have one child by a father who is not their husband, some have more than one child by the same man who is not their husband and others have multiple children by multiple men who are not their husband.
Some have one, then marry the father which these days legitimises the birth.

To even try to compute the chance that a child was not the child of the husband the figures would have to be far more detailed.
Cheers
Guy
PS This is not the same calculation for a dice as the dice having 6 sides has a limited number of possiblilities.

[KGarrad]

I think my family buck the trend?!

My paternal line has had just the 1 surname (and 1 spelling) from the mid-1500's.
Likewise, my maternal line (as far as my mother) have had the 1 surname, also since the mid-1500's.

[melba_schmelba]

If the supposed average rate of illegitimacy is 5% - does that mean, in 10 generations i.e. on average, about 300 years, the likelihood of your ancestor in the male line being someone of a different surname is 50%? And in 600 years, it is almost certain that one of your male ancestors would have had a father who was not who he was meant to be (or they inherited their mother's surname) ?

No, because the statistics do not show that they" show-" Illegitimate births accounted for 4–6 per cent of recorded births between 1860 and 1930 (40,000–65,000 a year).

So for the sake of simplicity round the percentage to 5%.

That is still not an average percentage of births by the married population as it includes many births by single women, in addition it does not take into account how many women have more than one illegitimate child, some have 5 or 6.

In a similar way some married women have one child by a father who is not their husband, some have more than one child by the same man who is not their husband and others have multiple children by multiple men who are not their husband.
Some have one, then marry the father which these days legitimises the birth.

To even try to compute the chance that a child was not the child of the husband the figures would have to be far more detailed.
Cheers
Guy
PS This is not the same calculation for a dice as the dice having 6 sides has a limited number of possiblilities.

Hi Guy, the 5% figure came from an estimation that is often quoted, although someone recently suggested 10% (can't remember who) and most people thought that figure was very much over the top. I would be including births by single women, in what I said, as the surname they would pass on to their son would usually not be that of the biological father, unless they later married or had the illegitimate birth accepted by the biological father, which was likely unusual. What I haven't included is adopted people, who often if not usually bear a surname that was not that of their biological father. But I think that would be a figure quite smaller than the illegitimacy rate, I think I found a 67 in 10000 figure earlier which is 0.67%, so it wouldn't affect my calculations too much.

[melba_schmelba]

I think my family buck the trend?!

My paternal line has had just the 1 surname (and 1 spelling) from the mid-1500's.
Likewise, my maternal line (as far as my mother) have had the 1 surname, also since the mid-1500's.

Ah but the point is you can't be sure that the biological father was a person of that surname in every birth of every ancestor on that male line . Well unless you are part of an in depth surname study, and you have verified that a very very distant cousin who shares the same surname and origins has the same Y-DNA profile.