When the probability model of an experiment is correct?

Suppose I wanted to tell what's the probability of event $A$: getting 2 tails in a row of 5 coin tosses. According to the classical definition of probability, the probability of this event is equal to number of cases favorable to it divided by the number of all possible cases. What if I said there's only one favorable case (getting 2 tails), and there are 5 possible outcomes in total (getting 1 tail, 2 tails, 3 tails, 4 tails, 5 tails). The probability is equal to $\frac{1}{5}$.

How to prove a model is incorrect with respect to the experiment we want to model in terms of probability, like in the example above?

What is our certainty that the 'correct' answer is indeed correct? The 'right' answer here is $$P(A)=\frac{5\choose 2}{2^{5}}$$

I don't have any objection regarding this answer, but it doesn't mean it's correct, right? One person saying it's OK doesn't prove its correctness.