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?

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?

J
240 points

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 $\big( \bigcup_1^\infty E_n \big)^c$

In an
jeffp

8.7k points

What is the sample space of this experiment?

The sample space is all possibilities of die rolls to obtain a six,

$$\{(6),(1,6),(2,6),(3,6),(4,6),(5,6),(1,1,6),(2,1,6),(3,1,6),\ldots,(1,2,6),(1,3,6),\ldots\}$$

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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