**Re: What is the difference between classical and bayesian understanding of probabilit**
Welp there is a metric ****-ton of articles about the difference, so it'd be worth reading up, but a very simple definition would be that a frequentist interprets

*probability* just how it's stated in your quote:

the relative frequency with which an event will occur if we repeated our "experiment" [a coin flip] a great many times.

This means that you can only usefully talk about the probability of events happening if you can at least imagine in principle conducting repeated "trials" (experiments, coin flips, whatever) in which sometimes the event takes place and sometimes it doesn't. To a frequentist, it's meaningless to ask what the probability it is that some hypothesis is true; the hypothesis is either true or it isn't (it isn't true in some trials and false in others). This is part of the reason why the probabilities we talk about in frequentism (e.g., p values) refer to how probable it is that a particular thing will be observed in an experiment, not how probable hypotheses themselves are. We can imagine conducting repeated experiments in which sometimes a thing happens and sometimes it doesn't. (But the hypothesis will simply remain either true or false).

In the Bayesian interpretation of probability, a probability is a state of certainty or belief with respect to some proposition. That probability could refer to the rate at which an event (e.g., a coin flip coming up heads) occurs over repeated trials, but it doesn't have to: A Bayesian can also refer to the probability that a particular hypothesis is true.

And Bayes theorem shows us how to combine existing knowledge/beliefs/information along with the data observed to make statements about probabilities.

(Note: That's a super simplistic version!)