Questions: A number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of rolling an even number. If there is more than one element in the set, separate them with commas. Sample space: Event of rolling an even number:

A number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of rolling an even number. If there is more than one element in the set, separate them with commas. Sample space: Event of rolling an even number:
Transcript text: A number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of rolling an even number. If there is more than one element in the set, separate them with commas. Sample space: $\square$ Event of rolling an even number: $\square$
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Solution

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Solution Steps

Step 1: Identifying the Sample Space

The sample space \(S\) for a die with 6 faces is \(S = \{1, 2, ..., 6\}\).

Step 2: Identifying the Event Outcomes

The outcomes for the specified event are \(E = \{2, 4, 6\}\).

Final Answer:

The probability of the event occurring is 0.5, calculated as \(\frac{|E|}{|S|} = \frac{3}{6}\).

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