My probability text distinguishes between two interpretations of probability values:
the frequency of occurrence "as percentage of success in a moderately large number of similar situations" (coin tosses, etc.), and
the likelihood of an occurrence of a unique event (whether a skier medals at Sochi, for example),
and argues that the latter conveys no information about the former, since it is a "one-time event".
If one considers the multiverse as a whole, however, are these interpretations still distinct? In particular, is the reason that a unique event has a likelihood that it occurs with the corresponding frequency across all universes? Does the answer depend on what kind of multiverse structure is being considered?
For example, is it the case that under a many-worlds interpretation of quantum mechanics, these are indeed equivalent, because the likelihood of an event is just the quantum mechanical distribution of possible events among "worlds"?