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Why did you switch from "mother who is a veteran" to "at least one parent is a veteran"?

SB: The headline of this piece said: "Boy born at 11:11 on 11-11-11 to vet on Vets Day." Most of the reports out there are not dealing with whether one or both of the parents are vets. It really doesn't matter. If the Dad is a vet and the Mum isn't, we would have read the same story.

I'll bet that the veteran status of P2 is heavily dependent on the veteran status of P1, that men are much more likely than women to be vets, that female vets of child-bearing age are more frequent than older vets...and so on. This is likely to be very from from a normal distribution in lots of ways.

Also it's very likely that obstetricians across the US gave the time of birth as 11:11 on 11/11/11 when it wasn't.

John: Clearly there are a lot more male vets than female vets out there, and one can follow the same logic to compute the probability of having a baby born to a mother who's a veteran.

The key here is to count the total number of ways in which a birth will generate this particular story, and for that, it doesn't matter whether the veteran is the mother or the father, nor the child a boy or a girl, etc.

Further to your last point, veteran parents are more likely to time their births to hit the target time so that too will make the use of average statistics too "pessimistic".

For an analysis of how birthdays in the US variy according to the time of year and day of the week, see
http://blogs.sas.com/content/iml/2011/09/09/the-most-likely-birthday-in-the-us/

There is also a "Holiday effect" to births (see http://blogs.sas.com/content/iml/2011/09/16/the-effect-of-holidays-on-us-births/), but since Veteran's Day is a "minor holidy," the effect isn't large.

I'd argue that the exact details of the calculation matter less than the fact that the "victory condition" was not set in advance.

EVERY childbirth, once selected, can be seen as an unlikely combination of odds: What are the odds that instead of being veterans, the parents had been fans of Calypso music, or could speak Dutch, or enjoyed salads? And what are the odds that a child of veterans (or of African Americans, or of Ohio residents) would be born on 11/11/11 at 12:11? or on 5/11/11 at 11:11? or on 7/14/1972 at 9:31? And so on.

This "veteran baby on 11:11" thing only became remarkable in retrospect, cherry-picking the supposedly relevant factors and ignoring all of the other "unusual" characteristics that are just as unlikely for any other baby born at any other moment. The fact that babies get born at all, despite all of these unlikely combinations, is a testament to the fact that, well, we have lots of babies and most of those factors are irrelevant.

Whether babies are more likely to be born on Fridays or whatever has little impact on it.

Adam: another way to put your point across is that there is a veteran baby born probably every minute of every day. the only thing that made this one newsworthy is that this particular Veterans day fell on 11-11-11.

Kaiser: Exactly. But it holds true even if there was only one veteran baby born every ten days, or one a month, or even one a year.

The 11/11 11:11 veteran baby only seems remarkable in retrospect. If you asked someone ahead of time, "What is the most remarkable trait (or combination of traits) that a baby could have if it was born on 11:11 at 11:11?", there are many things that may have seemed rarer and more remarkable than "veteran's baby." We're just seeing where the shot landed and then drawing the target around it.

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