This afternoon I heard a news story about a middle eastern country where one person said of the defenses for a stockpile of nuclear weapons, "even if there is only a 1% probability of the defenses failing, we should do more to strengthen them given the consequences of their failure".  I have nothing against this person's reasoning, but I do have an issue with where that 1% figure came from.

The statement above and others like it share a common problem:  they are phrased such that it's unclear over what probability space the measure was taken.  In fact, many journalist and other people don't seem especially concerned by this.  Even some commenters on Less Wrong give little indication of the probability space over which they give a probability measure of an event, and nobody calls them on it.  So what is this probability space they are giving probability measurements over?

If I'm in a generous mood, I might give the person presenting such a statement the benefit of the doubt and suppose they were unintentionally ambiguous.  On the defenses of the nuclear weapon stockpile, the person might have meant to say "there is only a 1% probability of the defenses failing over all attacks", as in "in 1 attack out of every 100 we should expect the defenses to fail".  But given both my experiences with how people treat probability and my knowledge of naive reasoning about probability, I am dubious of my own generosity.  Rather, I suspect that many people act as though there were a universal probability space over which they may measure the probability of any event.