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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.
Pair A: Rolling an even number Rolling a number smaller than 3
Pair B: Rolling an even number Rolling an odd number
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Answer
\boxed{\text{Pair B: Mutually exclusive, because there is no overlap between even and odd numbers}}
Step 1 ：Determine if there is any overlap between the events in each pair:
Step 2 ：Pair A: Even numbers (2, 4, 6) and Numbers smaller than 3 (1, 2) have an intersection: \(\{2\}\)
Step 3 ：Pair B: Even numbers (2, 4, 6) and Odd numbers (1, 3, 5) have no intersection
Step 4 ：Check if the events are mutually exclusive:
Step 5 ：Pair A: Not mutually exclusive, because they both include the number 2
Step 6 ：\boxed{\text{Pair B: Mutually exclusive, because there is no overlap between even and odd numbers}}
