Big Family Statistics!

As I announced a few days ago, the Murphy Family is expecting member #8 (or child #6, depending on how you’re counting).

My family has some interesting statistics. This is a geek blog, so why not have a little math geek fun?

Birth Order

Among my kids, all their birthdays are chronological along the year, starting “the year” with the birth of Baby #1. What I mean is that the first child’s birthday is in the middle of Fall, followed by the second’s birthday, then the third’s, in Winter, then the fourth’s in Spring, and then the fifth’s in Summer. It’s a funny sort of occurrence. Unfortunately, Baby #6 will interrupt this, due in Spring.

Let’s calculate some odds.

There was a 365/365 chance of Baby #1 coming on a day no previous baby had come on. So that’s 100%. Not really important.

Baby #2 could have come any of 364 days of the year still technically come after Baby #1, if the “year” is thought to start with Baby #1. So 364/365. Pretty good odds!

Baby #3 could have arrived on any of 345 days and still been #3 in both birth order and in a year started with Baby #1’s birth.

Baby #4 could have arrived on any of 295 days to retain this pattern.

Baby #5 could have arrived on any of 177 days.

Baby #6 — had the little booger been conceived a month or two later — could have arrived on any of 126 days.

But let’s go back to Baby #5. The odds of this birth-order-mirroring-order-of-birth-on-the calendar phenomenon, given the actual dates of birth of each previous child, is 36.94%. So a little over a third in our case. Of course, the odds would have been much better if we had kids celebrating birthdays each one day after the other, and much worse if, say, Baby #2 was born the day before Baby #1’s first birthday.

Boy-Girl

I remember an episode of the Simpsons, I think when they were expecting Maggie, where Bart confidently asserted his intellectual dominance over Lisa — *cough* — by informing her that children were born “boy, girl, boy, girl.”

In my family, this has been the case. Additionally, I’m older than my wife by just a few weeks. (Close enough that, as pro-lifers from conception to natural death, we aren’t really entirely sure which of us actually is older.)

The chance of any one member of my family being boy or girl is 50/50, of course. I’m generalizing, though; I believe there is some statistic that females are actually about 51% of the population, but this seems to me a flimsy statistic. I remember from college embryology that boys are more often miscarried than girls. I suspect more boys than girls die at a young age, too. I don’t know what age the survivors were when the 49/51 statistic was measured, but it seems the raw probability is really 50/50. Then again, some nations are killing off infant girls at an alarming rate — n.b., any rate is alarming — so perhaps I’m not grasping the truth of it. Anyway, for simplicity, I’m saying 50/50.

There are 8 slots in my family. The first slot is a 50% chance of their being a male, 50% female. The second slot is curious; it depends on the first slot. There is a 100% chance that the spouses in my family will be opposite sex. So we get a 50% probability for the first two slots taken together: either they are boy-girl or they are girl-boy.

There’s a simple 50% chance for each additional slot.

The probability of a family’s being boy, girl, boy, girl, boy, girl, boy, girl is 1/128, or 0.78%. That’s pretty small. Each possible arrangement of boys and girls in a family of 8 is the same: 1/128. What makes my family interesting is that it’s a repeated pattern, back and forth, seemingly organized this way on purpose, even though it’s completely random.

I figure there are maybe — totally guessing here — 10,000 8-member nuclear families in the United States. Probably fewer? If so, we could be one of fewer than 100 families nationwide with our family pattern. And we’re weirdo Catholics in a somewhat cramped, rural home.

Where do I sign up for my cable tv show deal? 😉 jk

EXCEPT we don’t know yet if we’re having a boy or a girl. We’ll know soon, I hope. Until then, we’re just a 1/64 family.

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