Contrary to what too many want to believe, probability theory does not define what “the probability” is. It only defines these (simplified) rules that the values must adhere to:
Every probability is greater than, or equal to, zero.
The probability of the union of two distinct outcomes A and B is Pr(A)+Pr(B).
The probability of the universal event (all possible outcomes) is 1.
Let A=”googolth digit of pi is odd”, and B=”googolth digit of pi is even.” These required properties only guarantee that Pr(A)+Pr(B)=1, and that each is a non-zero number. We only “intuitively” say that Pr(A)=Pr(B)=0.5 because we have no reason to state otherwise. That is, we can’t assert that Pr(A)>Pr(B) or Pr(A)<Pr(B), so we can only assume that Pr(A)=Pr(B). But given a reason, we can change this.
The point is that there are no “right” or “wrong” statements in probability. Only statements where the probabilities adhere to these requirements. We can never say what a “probability is,” but we can rule out some sets of probabilities that violate these rules.
Contrary to what too many want to believe, probability theory does not define what “the probability” is. It only defines these (simplified) rules that the values must adhere to:
Every probability is greater than, or equal to, zero.
The probability of the union of two distinct outcomes A and B is Pr(A)+Pr(B).
The probability of the universal event (all possible outcomes) is 1.
Let A=”googolth digit of pi is odd”, and B=”googolth digit of pi is even.” These required properties only guarantee that Pr(A)+Pr(B)=1, and that each is a non-zero number. We only “intuitively” say that Pr(A)=Pr(B)=0.5 because we have no reason to state otherwise. That is, we can’t assert that Pr(A)>Pr(B) or Pr(A)<Pr(B), so we can only assume that Pr(A)=Pr(B). But given a reason, we can change this.
The point is that there are no “right” or “wrong” statements in probability. Only statements where the probabilities adhere to these requirements. We can never say what a “probability is,” but we can rule out some sets of probabilities that violate these rules.
Even if this was true, I don’t see how it answers my question.