Because the material isn't quite the same, and because different people have different teaching and learning styles. The material isn't quite the same because

Because the material isn't quite the same, and because different people have different teaching and learning styles. The material isn't quite the same because your ideas of what a first-year student needs to learn about probability may differ from someone else's. Not just because your and their prejudices are different: it'll be influenced by what else is in other courses. Imagine two universities with first-year probability courses for their mathematicians. One of them also has a statistics course that everyone takes, the other doesn't. They may make different choices about what goes in the probability course. And it'll be influenced by the students they get. Imagine one of the universities is a very prestigious highly-selective one that lots of good mathematicians apply to, and the other ... isn't. The first will likely want more material in their course. Now, think again about those last two universities. As well as possibly presenting different material, they may well want it presented differently. Fancypants University will want extra-rigorous proofs, connections to other fields of mathematics (measure theory, probabilistic methods in combinatorics, ...), more challenging problems. Slowcoach Polytechnic will want a very clear and straightforward presentation that doesn't leave anything unexplained and doesn't distract students with irrelevancies. So even when they're presenting the same material, the approaches required will be different. Different students will want different things, too. Besides the sort of differences in the previous paragraph (which of course apply between students as much as they do between universities), some students will be interested in the foundations of the subject (what is a probability, anyway?) and some won't; some will be interested in particular kinds of applications; some will like thinking visually and benefit from a lot of digrams, some will find them distracting; etc., etc., etc. Now, with all that in view, imagine you're a professor who's teaching Probability 101 for the first time next year. No matter what, you're going to need to do a lot of thinking about what material you put in your lectures, how you divide it up, how you want to present it, etc. You're going to need some notes for your benefit. (The benefit comes both from making them and from having them.) The extra effort required to polish them up and make them usable by students too is actually pretty small. The fact that other people have presented other similar courses and made similar notes is neither here nor there. You can't just take their notes and avoid all the effort, because their course isn't identical to yours, and their students aren't identical to yours, and their style of presentation isn't identical to yours, and much of the benefit of making the notes comes from actually making them. So, you make your own notes, and then you might as well put them on the internet. And here we are.