TITLE: A die is rolled until a 6 comes up. Should the sample space of this experiment contain the set of all infinite sequences which do not contain a 6?
QUESTION [5 upvotes]: 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?

REPLY [2 votes]: Since you (might) need to account for the hypothetical event that a 6 is never rolled, I would go ahead and say that Brian M. Scott is more or less correct - in plain terms, the sample space is the set of all finite sequences terminating in a 6 and all infinite sequences containing no 6. If the zero-probability event that a 6 is never rolled is irrelevant, then it doesn't matter too much, as Ross Millikan points out in another answer.