Let's examine each event and determine which outcomes meet the criteria:

Given Outcomes:

The possible outcomes when a number cube is rolled three times are:

• EOO
• OEE
• EEE
• OOO
• OEO
• EEO
• OOE
• EOE

Event A: More odd numbers than even numbers

For this event, we need outcomes where the count of odd numbers is greater than even numbers.

• EOO, OOO, OEO, OOE

So, check these outcomes for Event A.

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

For this event, the first two rolls need to be odd numbers.

• OOO, OOE

Check these outcomes for Event B.

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

For this event, we need outcomes where either the first roll, the second roll, or both are even.

• EOO, OEE, EEE, EEO, EOE

Check these outcomes for Event C.

Probability Calculation

Each outcome has an equal probability. Since there are 8 possible outcomes, the probability of each event is calculated by counting the successful outcomes and dividing by 8.

1. Event A: 4 successful outcomes → Probability = $\frac{4}{8} = 0.5$
2. Event B: 2 successful outcomes → Probability = $\frac{2}{8} = 0.25$
3. Event C: 5 successful outcomes → Probability = $\frac{5}{8} = 0.625$

Would you like a more detailed breakdown of each step?

Related Questions:

1. How would the outcomes change if the die had a different number of sides?
2. What if we added another roll, making it four rolls instead of three?
3. How does the probability change if each outcome is not equally likely?
4. What is the probability of rolling all even numbers?
5. How could we represent these outcomes and events using Venn diagrams?

Tip:

For any probability problem, start by defining the sample space and identify which outcomes satisfy each event for clarity.