Let’s analyze the events and the outcomes listed for each event. Here’s a breakdown of each event and how it matches the outcomes provided:

1. Event A: An odd number on each of the first two rolls

   • We need outcomes where both the first and second rolls are odd.
   • Possible outcomes: $OOO$ and $OOE$ (only outcomes with odd numbers in the first two positions).

2. Event B: No even numbers on the first two rolls

   • This means that both the first and second rolls must be odd, leaving us with the same outcomes as Event A.
   • Possible outcomes: $OOO$ and $OOE$.

3. Event C: Exactly one odd number

   • This requires only one "O" (odd) across all three rolls.
   • Possible outcomes: $EOO$, $OEE$, and $EEO$.

Next, let's assign the probabilities:

• Since there are 8 outcomes in total, each has a probability of $\frac{1}{8}$.
• For each event, count the selected outcomes and multiply by $\frac{1}{8}$ to get the event's probability.

Here's how the table should look:

Please let me know if you'd like a deeper breakdown or if you have specific questions!

Additional Questions:

1. What would be the probability if we had four rolls instead of three?
2. How would the outcomes change if we considered only even numbers?
3. What is the total probability for mutually exclusive events in this scenario?
4. Could we calculate the odds for getting two even numbers in any order?
5. What if we wanted exactly two odd numbers?

Tip: When calculating probabilities, ensure each outcome has an equal chance to maintain accurate results.