Let's examine the events and outcomes one by one to complete this table.

The outcomes are listed as sequences like "OOE" (Odd-Odd-Even), representing the result of three dice rolls.

Event A: "An even number on the second roll or the third roll (or both)"

To satisfy this event, the second or third roll (or both) should be even. The relevant outcomes are:

• OOE (third roll even)
• OEO (second roll even)
• EEO (second and third rolls even)
• EOE (second and third rolls even)
• EEE (second and third rolls even)

So, check these five outcomes for Event A.

Event B: "Exactly one odd number"

For exactly one odd number, only one of the three rolls should be odd. The relevant outcomes are:

• EOO (first roll odd)
• OEE (second and third rolls even)

Check these two outcomes for Event B.

Event C: "An even number on the second roll"

For this event, the second roll must be even. The outcomes satisfying this condition are:

• OEO
• EEO
• EOE
• EEE

Check these four outcomes for Event C.

Probability Calculation

Since there are 8 possible outcomes in total, the probability of each event can be calculated as: $\text{Probability} = \frac{\text{Number of favorable outcomes}}{8}$

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

Would you like further details or help with related questions?

Related Questions:

1. What would be the probability if the cube was rolled four times instead of three?
2. How would the probabilities change if only odd outcomes were considered for each roll?
3. Could the probabilities be impacted by using a biased die?
4. How can we extend these calculations for a higher number of rolls?
5. What are the odds of getting all even rolls or all odd rolls?

Tip:

When calculating probabilities, ensure all possible outcomes are accounted for to avoid overestimating or underestimating results.