Question

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 the number 1, 3, or 4. if there is more than one element in the set, separate them with commas. sample space: {} event of rolling the number 1, 3, or 4 : {}

Explanation:

Step1: Determine the sample space for a die roll

A standard die has 6 faces, numbered 1 through 6. So the sample space (all possible outcomes) when rolling a die is the set of numbers 1, 2, 3, 4, 5, 6.
$$\{1, 2, 3, 4, 5, 6\}$$

Step2: Determine the event of rolling 1, 3, or 4

We need to list the outcomes that are 1, 3, or 4 from the sample space. So we pick those three numbers.
$$\{1, 3, 4\}$$

Answer:

Sample space: $\{1, 2, 3, 4, 5, 6\}$
Event of rolling the number 1, 3, or 4: $\{1, 3, 4\}$