Oscar_Cunningham comments on Bayes' rule =/= Bayesian inference - Less Wrong
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Pedantry alert: This is not technically true, although it's still a very important point.
Every frequency is the probability of something; in this case, the frequency with which the coin comes up heads is the probability, given that you pick one of the times that the coin is flipped, that coin comes up heads that time.
But this is not the same thing as the probability that the coin comes up heads the next time that you flip it, which is what you are more likely to be interested in (and which people are liable to uselessly claim is "either 1 or 0, but I don't know which").
Thanks, this clears some things up for me.
You're welcome!