The problem involves analyzing a single roll of a six-sided number cube (standard die), and we need to identify two things:

1. The sample space: This is the set of all possible outcomes when rolling the die.
2. The event of rolling a number from 2 to 4: This subset of the sample space includes only outcomes satisfying the condition of being between 2 and 4.

Solution:

• Sample space: Since the die has six sides labeled from 1 to 6, the sample space is: $\{1, 2, 3, 4, 5, 6\}$

• Event of rolling a number from 2 to 4: This includes the numbers 2, 3, and 4. Hence, the set for this event is: $\{2, 3, 4\}$

Would you like further explanations or help with other parts of this problem?

Follow-up Questions:

1. How would the sample space change if the number cube had more than six sides?
2. What is the probability of rolling a number between 2 and 4?
3. What is the complement of the event of rolling a number between 2 and 4?
4. How would we represent the event mathematically in set notation?
5. How would probabilities differ if the die were weighted (not fair)?

Tip:

Always ensure that the sample space comprehensively includes all possible outcomes, as any missing element could affect probabilities and calculations.