Can we say the frequentist interpretation of probability is more appropriate in the dice rolling problem? Suppose we role a dice and see what we get, the sample space is $\{1,2,3,4,5,6\}$ and each outcome occurs with probability 1/6. For example, if we look at the probability that 6 appears, it seems natural to interpret the probability of 1/6 as $plim \frac{n_6}{n}$ where $n$ is the total number of trials and $n_6$ is the number of times we get a 6. That is to say, the frequentist interpretation of 1/6 as the limiting frequency seems natural. This is also something that could be verified using repeated experiment.
My questions are:

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*In this example, how to take a Bayesian interpretation of the probability 1/6?  Is the Bayesian interpretation less appropriate/suitable in this example compared to the frequentist interpretation?


*In general, is it true that the Bayesian interpretation of probability makes more sense under certain scenarios, while the frequentist interpretation of probability is better in other scenarios?

If you know that the die is fair, then this can equally be viewed as a Bayesian interpretation with a dogmatic prior that puts all prior probability on the die being fair, so one could argue that the Bayesian interpretation does equally well.
If, on the other hand, the die is not fair, then, if you have prior knowledge on the sense in which it is not fair, you may improve your inference over the frequentist estimator $n_6/n$, especially when $n$ is "small".
