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 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: Define sample - space

The sample - space is the set of all possible outcomes when rolling the number cube. Since the cube has faces labeled 1 to 6, the sample - space is all numbers from 1 to 6.
{1, 2, 3, 4, 5, 6}

Step2: Identify event outcomes

The event is rolling the number 1, 3, or 4. So the outcomes for this event are just 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}