Go Ahead and Count 'Em... Four Boys!

Living in the South, you meet a fair number of large families.  I never felt like a statistical anomaly when I had three boys.  After we had our fourth son, however, my husband and I began noticing the stares from onlookers, followed by silent (and in many cases, not so silent) counting.  The typical reaction is for strangers to glance at our family, and then glance again; count the number of boys; and finally ask the gender of the baby just to be certain.  The last part of this exchange usually involves some words of consolation or sympathy from the onlooker, proceeded by one of the following three questions:
 

1. "So are you going to try for a girl?"

2. "Are all of these your biological children?" or

3. "Was the last one an accident?"

The first time this happened to us, we didn't think much of it.  Now, after numerous times that strangers have approached us to remark on the number of boys we have, we are starting to realize the novelty of it.  So math nerd that I am, I decided to figure out the percentage of Americans who have four boys.

First, I calculated the statistical probability of having four boys.  Every birth is an independent event, which means you have a 50% chance of having a boy at each pregnancy.  By the fourth pregnancy, one still has a 50% chance of having a boy, but the odds that all four children are boys is 50% x 50% x 50% x 50% = 6.25%.    

Next, I had to figure out how many Americans have four children.  Unfortunately, the U.S. Census Bureau only releases data for households with "three or more children".  The most recent census indicates 9% of American households have at least three children.  If you adjust for all children in one household having the same biological parents (compared to blended families), the percentage goes down to 7.47%.

Then I found a study published in The New York Times based on census data combined with other demographic research, which indicates that 0.78% of American households are comprised of a married couple with four children under the age of 18 years.  However, this figure doesn't include unmarried couples with four children; single parents with four children; couples (married or unmarried) whose four children are not all under 18 years of age; and parents who don't reside with all four children.

So, assuming the actual number I want is somewhere between The New York Times' narrowly determined 0.78% and the U.S. Census Bureau's catchall 7.47%, I averaged the two numbers.   The result, 4.125%, wasn't scientifically derived, but it was sufficient to satisfy my curiosity.   

Lastly, to figure out the number of households with four children who are all boys, I multiplied 4.125% by 6.25%.  The end result: Only 0.2578125% of Americans have four sons.  A quarter of one percent. 

We're in a small subset of the population.

So now I can appreciate why people feel the need to remark on the number of boys that are crammed into and hanging off our double wide stroller like monkeys around a tree branch.  I still don't care for the offer of sympathy or nosy questions, but I understand why having four boys is noteworthy.

And as for the counting?  That part was always easy to understand.  I know they're fast, and if you blink you might miss one.