4
votes
3answers
177 views

Do the Kolmogorov's axioms permit speaking of frequencies of occurence in any meaningful sense?

It is frequently stated (in textbooks, on Wikipedia) that the "Law of large numbers" in mathematical probability theory is a statement about relative frequencies of occurrence of an event in a finite ...
3
votes
6answers
198 views

Logical issues with the weak law of large numbers and its interpretation

In several probability textbooks I have found what amounts to the following argument: Let A be an event in some probabilistic experiment. Let p=P(A) be the probability of this event occurring in ...
2
votes
3answers
106 views

Regarding the validity of probability theory [closed]

Imagine I have a regular balanced dice and i roll it once. It is assumed that the probability of any number (1-6) is 1/6. However, isn't this just an illusion we are feeding ourselves for our lack of ...
2
votes
1answer
112 views

Is there a probability interpretation that only allows for probabilities in $\left[0,1\right]\cap\Bbb Q$?

Are there probability interpretations that only allow for probabilities that are members of the set $$\left[0,1\right]\cap\Bbb Q?$$ Related, but distinct: Allowed probabilities under frequentism.
4
votes
2answers
87 views

Allowed probabilities under frequentism

Am I right to assume that under the frequentist interpretation of probability,* the set of allowed probabilities isn't $$\left[0,1\right],$$ but rather is ...
8
votes
5answers
545 views

Successful approaches to the modelization of ''randomness''

If you pick a number $x$ randomly from $[0,100]$, we would naturally say that the probability of $x>50$ is $1/2$, right? This is because we assumed that randomly meant that the experiment was to ...
6
votes
4answers
308 views

Is probability objective?

As we know, probability is a measure of events. However, is it an objectively attribute of events, or just an illusion in ones' mind? For example, suppose that there is an empty black box with an ...
3
votes
1answer
335 views

Probability and Axiom of Choice

I'm not a logician, so I apologize if what follows translates to nonsense. I would like to try to define a different theory of random choice. I hesitate to call it probability theory because I do not ...
2
votes
4answers
371 views

Evidence of Absence = Absence of Evidence?

Any clever-cloggs out there who can explain the formula below in more simple English please? - Do you agree with the formula?