Question

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 a number from 2 to 4. if there is more than one element in the set, separate them with commas. sample space: event of rolling a number from 2 to 4 :

Explanation:

Step1: Determine the sample space

The number cube has faces labeled \(1\) to \(6\). So the sample space \(S\) is the set of all possible outcomes when the cube is rolled.
\(S=\{1,2,3,4,5,6\}\)

Step2: Determine the event of rolling a number from \(2\) to \(4\)

We need to find the numbers \(x\) such that \(2\leq x\leq4\) and \(x\in S\).
The numbers that satisfy this condition are \(2\), \(3\), and \(4\). So the event \(E\) (rolling a number from \(2\) to \(4\)) is \(E = \{2,3,4\}\)

Answer:

Sample space: \(\{1,2,3,4,5,6\}\)
Event of rolling a number from \(2\) to \(4\): \(\{2,3,4\}\)