Application of Probability Theory in IT

It so happened that I teach students of IT-shnyh specialties in the Siberian Federal University (SFU) subject such as "Theory of probability and mathematical statistics." From year to year I come across such a phenomenon that students do not understand why and why they should learn this discipline. Of course, we can say that mathematics trains the brain and develops abstract thinking (which is very necessary for programmers). But I think that if you reinforce the teaching of TV and MS with vivid examples (especially in relation to IT), this will provide the necessary motivation to study this subject.

What examples I give:

1. All students are now playing. In most games, there is an element of chance in one form or another, for example, the chance of dropping a valuable bonus from a defeated enemy. Accordingly, I say to students: “See, the programmers of this game used elements of probability theory.”
2. Modeling all processes. For example, as I saw a program about modeling a fire at a stadium and crowd behavior. Without probability theory there is nowhere.
3. Generate random passwords.
4. Prediction of transitions in the pipeline of modern processors.
5. Interference-free coding algorithms.

All these examples impress students. They, of course, do not begin to hard teach the terver, but at least do not ask stupid questions anymore, “Why do we need to learn all this?”.

I would like to replenish the collection of illustrative examples of the use of TV in IT. Maybe someone else will come in handy. Who else can add - write to comments.