Is it correct to think that the true probability of an event cannot be ever known?
When studying probability, in the first lectures, there are those typical exercises which start with sentences like: "One tosses a (fair) coin." or "In a bag there are 4 blue marbles and 6 red marbles.". In the first case we usually say that $P($heads$)=0.5$ and in the latter: $P($blue marble$) = 0.4$.
After a few lectures, there comes the notion of "maximum likelihood estimation" (MLE) and one can observe that in the second case above (with marbles) we just fit a Bernoulli distribution to the data we had (10 marbles: BBBB RRRRRR).
I don't know how to think about the first example above (with coin tossing). But I have the following intuition (which would help me a lot I guess) and I hope you can help me to understand if I am correct or not:
The true probability of an event cannot be ever known.
In the first case (with coin tossing) the probability was estimated from context/text. Can we say that I applied the closed world assumption?
In the second case (with marbles) the probability was estimated from data (using MLE).
As a conclusion, the probability cannot be known, but can be assumed to be some number. My two examples were not examples of estimating probabilities (because there was NO data: I incorrectly said that the marbles were data...), but of making someone to think of a specific assumption: equally likely outcomes assumption.