Let's go through each event in the table to identify the correct outcomes and probabilities.

Step-by-Step Analysis:

1. Possible Outcomes:

   • The outcomes listed in the table are combinations of odd (O) and even (E) rolls: EOO, OEE, EEE, OOO, OEO, EEO, OOE, EOE.

2. Event A: More odd numbers than even numbers

   • For an outcome to have more odd numbers than even, at least two out of the three rolls should be odd.
   • The outcomes that satisfy this condition are: EOO, OOO, OEO, and OOE.
   • Probability = $\frac{4}{8} = 0.5$.

3. Event B: An odd number on each of the first two rolls

   • This event requires that both the first and second rolls are odd.
   • The outcomes that meet this requirement are: OOO and OOE.
   • Probability = $\frac{2}{8} = 0.25$.

4. Event C: An even number on the first roll or the second roll (or both)

   • This event is satisfied if the first roll is even, the second roll is even, or both.
   • The outcomes that match this criterion are: EOO, OEE, EEE, EEO, and EOE.
   • Probability = $\frac{5}{8} = 0.625$.

Final Table Fill-In:

Let's populate the table based on our findings.

Would you like additional clarification on any step?

Here are some additional questions you might consider:

1. How would probabilities change if the cube was rolled four times instead of three?
2. What if the probabilities were not equal for each outcome?
3. Could you determine the outcomes for each event if each roll was a different type of die?
4. How would Event A change if it required an equal number of odd and even outcomes?
5. What is the probability of getting exactly one even number in three rolls?

Tip: When calculating probabilities, ensure all possible outcomes are accounted for to avoid underestimating or overestimating the total probability.