## Archive for September 6, 2012

### Kindergarten Math

Alex and Eli started kindergarten on Tuesday.

At a “Meet the Teacher” event last week, we were told that this is the most kindergarten classes they’ve had at the school. “We had to add another class this year, so we now have eight,” one of the teachers said.

“How many students are in each class?” I asked.

“Twenty-one,” she said, “so it’s really good that we added that eighth class — or else there’d be, like, 26 students in each class!”

I was too polite to tell her that 8 × 21 ≠ 7 × 26.

Today, we had a parent-teacher conference. On the bulletin board in her class was the following chart with student names:

There are 19 students in the class, and all of them have a first name that that begins with a letter in the first half of the alphabet. There are 3 A’s, 1 B, 3 C’s, 1 D, 2 E’s, 1 I, 3 K’s, 3 L’s, and 1 M.

I mentioned this to the teacher. “I know!” she said. “Isn’t that an amazing distribution!”

*Well, yeah*, I thought. *It’s quite amazing, in fact.*

If you assume that names are evenly distributed across the alphabet, the probability that all 19 students would have a first name in the first half of the alphabet is an astounding (1/2)^{19} = 0.00000002%.

But of course, names are not evenly distributed across the alphabet. I don’t know how they’re distributed, but the first letters of English words are distributed as follows:

That means that 52.005% of all English words start with a letter in the first half of the alphabet. If you assume that names follow the same distribution, then the probability doubles to 0.00000004%.

Yup. Still pretty low.