Example 1.1.2.
An experiment consists of rolling a standard 6-sided die. The sample space is \(\Omega = \{1, 2, 3, 4, 5, 6\}\text{.}\) One possible event is \(A = \{2, 4, 6\}\text{,}\) i.e., the event that the result of the roll is even.
What would the sample space look like if we roll the die two times and recorded the results?
Answer.
\begin{align*}
\Omega = \{\amp (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), \\
\amp (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), \\
\amp (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), \\
\amp (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), \\
\amp (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), \\
\amp (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)\}
\end{align*}
Note that, for example, \((1, 2)\) is a different outcome from \((2, 1)\text{.}\)