Lola rolls a fair six-sided dice. For each pair of events below, decide whether the events are mutually exclusive. If the events are not mutually exclusive, give an example to show why.
\begin{tabular}{c|l}
Pair A: & $\begin{array}{l}\text { Rolling an even number } \\
\text { Rolling a number smaller than } 3\end{array}$ \\
\hline Pair B: & $\begin{array}{l}\text { Rolling an even number } \\
\text { Rolling an odd number }\end{array}$ \\
\hline Pair C: & $\begin{array}{l}\text { Rolling an even number } \\
\text { Rolling a prime number }\end{array}$ \\
\hline
\end{tabular}
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Answer
\boxed{\text{Pair C: Not mutually exclusive}}
Step 1 ：Pair A: Even numbers: \(\{2, 4, 6\}\), Numbers smaller than 3: \(\{1, 2\}\), Intersection: \(\{2\}\)
Step 2 ：Pair B: Even numbers: \(\{2, 4, 6\}\), Odd numbers: \(\{1, 3, 5\}\), Intersection: \(\emptyset\)
Step 3 ：Pair C: Even numbers: \(\{2, 4, 6\}\), Prime numbers: \(\{2, 3, 5\}\), Intersection: \(\{2\}\)
Step 4 ：\boxed{\text{Pair A: Not mutually exclusive}}
Step 5 ：\boxed{\text{Pair B: Mutually exclusive}}
Step 6 ：\boxed{\text{Pair C: Not mutually exclusive}}
