One of the things that fascinates me is that after studied and used probability and statistics, quantum physics seems to have a different approach to the world of probability. The only common point I find is that the probability of an event must bee somewhere between 0 and 1, and that's it, that's the only one.
https://www.scottaaronson.com/democritus/lec9.html
“Now, what happens if you try to come up with a theory that's like probability theory, but based on the 2-norm instead of the 1-norm? I'm going to try to convince you that quantum mechanics is what inevitably results.
Let's consider a single bit. In probability theory, we can describe a bit as having a probability p of being 0, and a probability 1-p of being 1. But if we switch from the 1-norm to the 2-norm, now we no longer want two numbers that sum to 1, we want two numbers whose squares sum to 1.”