# Classrooms With 500,000 Students

I am fascinated by the Stanford online courses in machine learning and artificial intelligence. My first inkling of them came when quite a few of my students started taking the artificial-intelligence class. Olin is very small, only about 400 students, so I realized that these online courses must be large. But I almost fell over when I saw that enrollment varied from 66,000, at the low-end, to 160,000.

Sebastian Thrun, who co-taught the artificial-intelligence course to 160,000 students, is now leaving Stanford teaching in order to teach courses to 500,000 students for free. What an inspiring goal!

My only complaint, due to my habit (or handicap) of thinking about every number that I come across, is with the comments on the number of perfect scores. Here are the data: Of the 160,000 students, 248 students got a perfect score, and none was among the 200 Stanford students. These data have been widely reported with the implication that the Stanford students were less successful than the online students.

As a Stanford graduate, I needed an alternative model. Thus, imagine a pool of 160,000 students, among whom 200 are at Stanford. Now strew 248 perfect scores among the 160,000 students randomly.

What is the probability that no perfect score lands on a Stanford student?

This probability turns out to be almost exactly 0.73 (a reasonable approximation to it is 1 – 200*248/160000, or 0.69). Thus, assuming only that all students are equally likely to get perfect scores, it is quite probable (a 73-percent probability) that no Stanford student will have a perfect score. It’s not that they are any different from the other students; there just aren’t enough of them.

Which brings us back to Thrun’s reason for teaching outside the university. From his talk at the DLD 2012 conference (at about the 20-minute mark in the video):

Having done this, I can’t teach at Stanford again…It’s impossible…there’s a red pill and a blue pill and you can take the blue pill and go back your classroom and lecture your 20 students. But I’ve taken the red pill and seen Wonderland.

I wish Thrun every success making knowledge and understanding so widely available.