A die is rolled continually until a 6 appears, at which point the experiment stops. What is the sample space of this experiment?
Let $E_n$ denotes the event that $n$ rolls are necessary to complete the experiment. What points of the sample space are contained in $E_n$?
What points of the sample space are contained in $(\bigcup_{i=1}^{\infty}E_n)^\mathsf{c}$?