@FStratford, I simplified it for the sake of clarity, but you’re right that if these were all the courses offered it wouldn’t work mathematically.
My point was that % of large vs. small classes doesn’t mean a lot unless you know the actual size of the classes. If you want to know a student’s chance of ending up in a large or a small class, instead of dividing the total number of classes by the number of large classes you need to divide the number of total seats by the number in any one class.
Take UCB’s monster 1000-student CS course, for example. It’s only one out of the plethora of classes offered at UCB, but if the course is offered once a year an average UCB student would have a one in eight chance of being in this one class during their undergrad years. If it’s offered in both the fall and spring the chances rise to one in four.
To be clear, I don’t think there’s anything wrong with some large classes, and I don’t think smaller necessarily means better. I’d rather be in an English or philosophy discussion with fifteen students than three. It’s also not random. A CS, economics or psychology major is more likely to end up in large classes than a Russian or religion major.