$A$ die is thrown repeatedly until a six comes up. What is the sample space for this experiment?
In this experiment,the die is thrown until a $6$ appears. Let $S$ denote the sample space.
If $6$ appears on the first throw,the outcome is $6$.
If $6$ appears on the second throw,the outcome is $(x, 6)$ where $x \in \{1, 2, 3, 4, 5\}$.
If $6$ appears on the third throw,the outcome is $(x, y, 6)$ where $x, y \in \{1, 2, 3, 4, 5\}$.
Continuing this process,the sample space $S$ is given by:
$S = \{6, (x, 6), (x, y, 6), (x, y, z, 6), \dots \}$ where $x, y, z, \dots \in \{1, 2, 3, 4, 5\}$.
If $6$ appears on the first throw,the outcome is $6$.
If $6$ appears on the second throw,the outcome is $(x, 6)$ where $x \in \{1, 2, 3, 4, 5\}$.
If $6$ appears on the third throw,the outcome is $(x, y, 6)$ where $x, y \in \{1, 2, 3, 4, 5\}$.
Continuing this process,the sample space $S$ is given by:
$S = \{6, (x, 6), (x, y, 6), (x, y, z, 6), \dots \}$ where $x, y, z, \dots \in \{1, 2, 3, 4, 5\}$.
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