Yahoo! news tell us that it is "remarkable" that a baby born at 11:11 on 11-11-2011 (Veterans' Day) was born to a mother who was a veteran.
But how truly remarkable is this?
Here's how to think about this: How many babies are born at 11:11 on 11-11-2011? And what's the likelihood that a baby is born to parents at least one of whom is a veteran?
According to the CDC (link to PDF here), the average number of babies born on an average Friday in the U.S. in 2009 was 12,364. Next, say 12,500 babies were born today, what proportion of these babies would have at least one parent who is a veteran? From the Census 2000 data, we learn that about 13% of civilians over 18 are veterans. Assuming that veterans are equally likely to have children as non-veterans, then about 13% of those 12,500 babies would be born to veterans, or 1625 babies.
It would be great to know the distribution of these births throughout the day but the time of day data does not seem to be available. If births are uniformly distributed throughout the 24 hours (or 1440 minutes), then there are 1.13 babies born per minute to veterans.Yahoo! tells us they located the one baby born at 11:11 precisely.
That's a start. Some refinements are possible. For example, since only one of the two parents need be a veteran, the probability that a baby would have at least one veteran parent is actually higher than 13%. The probability of neither parent being a Veteran is (1-0.13)*(1-0.13) = 76% so the probability of at least one veteran parent is 24%. This calculation assumes that one parent being veteran is independent of the other parent being veteran, which also may require refinement but I'll leave it at that. Using 24% instead of 13% would attribute 3,000 births a day to veteran parents.
The 13% is an overestimate because over 18 is not the same as child-bearing age. And of course, the assumption of births uniformly distributed throughout the day is almost surely wrong. For example, it is believed that more C-sections happen on Fridays as doctors would rather not operate over the weekend, and one could imagine that these births, if they are not emergencies, are more likely to take place in the middle of the day than say late at night. (See, for instance, this article which concluded "Nonacute C-sections (70% cephalopelvic disproportion) were not performed as frequently at night (12-8 A.M.) as at other times at three of the four hospitals".)