To construct the sample space and the specific event space needed for this problem, we need to identify the possible outcomes for rolling a six-sided number cube (commonly known as a die) and then list the outcomes that correspond to rolling a number from 2 to 4 inclusive.
**Sample Space:**
A six-sided number cube has six faces, each with a distinct number from 1 to 6. When you roll the cube once, any one of these six numbers can come up. Therefore, the sample space, which is the set of all possible outcomes of this random experiment, is as follows:
Sample space: {1, 2, 3, 4, 5, 6}
**Event of Rolling a Number from 2 to 4:**
An event is a specific subset of the sample space that we are interested in. In this case, we are interested in the event where the outcome of rolling the number cube is a number from 2 to 4. The outcomes that correspond to this event are just the numbers 2, 3, and 4 because those are the only numbers within the range of 2 to 4 that can appear on the faces of our cube.
Event of rolling a number from 2 to 4: {2, 3, 4}
To sum up:
Sample space: {1, 2, 3, 4, 5, 6}
Event of rolling a number from 2 to 4: {2, 3, 4}
