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The example is not quite right. The Bayesian starts with a prior, some weighting of likelihoods. In the case of a coin a reasonable prior would place a lot of initial probability on the coin being fair or almost fair. You'd need to flip a biased coin more times in order to overcome the prior and make 'biased' the dominant hypothesis.

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That is correct. I tried to allude to that in the end when I said how a Bayesian mysteriously gives a certain confidence to the space of models. In the case of a uniform prior I believe my example is correct.

Usually when Bayesian probability is explained, it often comes across as "duh, that's what anyone would do" except not rigorously with equations. I tried to give an example contrasting a Frequentist and Bayesian approach.

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