Is there a standard way to view this? The problem is,
In an experiment, die is rolled continually until a 6 appears, at which point the experiment stops. What is the sample space of this experiment?
My first instinct was to say that it was the set of all finite sequences with exactly one 6, which is in the final position. But this neglects the (zero-probability) event that a 6 never comes up. Should this be in the sample space? Does it matter?