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? Let En denote the event that n rolls are necessary to complete the experiment. What points of the sample space are contained in En? What is $\big( \bigcup_1^\infty E_n \big)^c$
What is the sample space of this experiment?
The sample space is all possibilities of die rolls to obtain a six,
What points of the sample space are contained in $E_n$?
This is all possible die rolls which end in a six. Where $\bigcup_1^\infty E_n$ is all possibilites.
What is $\bigg( \bigcup_1^\infty E_n\bigg)^c$?
$\bigg( \bigcup_1^\infty E_n\bigg)^c$ is the empty set, since a six must happen eventually
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