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Regarding the philosophical objections about the probability of
after-the-fact events, I think such objections may be allayed by a simple
rewording of the question so it refers to potential events instead of those
which have already happened. Also, such objections lose their force anyway if
only a more Bayesian interpretation of the probabilities involved is used
(which I prefer, BTW). After all, the whole point of the problem is to
illustrate the effect of how conditional probabilities depend on additional
information.