Let's analyze each event and determine the outcomes that meet the conditions described.

Outcomes List

The outcomes are as follows:

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

Each outcome is represented by three letters, where:

• "E" stands for an even number.
• "O" stands for an odd number.

Event A: "Two or more even numbers"

To satisfy this event, at least two of the three rolls must be even. The outcomes that meet this condition are:

• EOE
• OEE
• EEE
• EEO

Thus, check the boxes for EOE, OEE, EEE, and EEO. The probability of Event A is the count of favorable outcomes divided by the total number of outcomes: $\text{Probability of Event A} = \frac{4}{8} = 0.5$

Event B: "An even number on both the first and the last rolls"

To satisfy this event, the first and third rolls must be even. The outcomes that meet this condition are:

• EOE
• EEE
• EEO

Thus, check the boxes for EOE, EEE, and EEO. The probability of Event B is: $\text{Probability of Event B} = \frac{3}{8} = 0.375$

Event C: "An odd number on each of the last two rolls"

To satisfy this event, the second and third rolls must be odd. The outcomes that meet this condition are:

• OOE
• OOO

Thus, check the boxes for OOE and OOO. The probability of Event C is: $\text{Probability of Event C} = \frac{2}{8} = 0.25$

Summary of Answers

• Event A: Outcomes EOE, OEE, EEE, EEO, Probability = 0.5
• Event B: Outcomes EOE, EEE, EEO, Probability = 0.375
• Event C: Outcomes OOE, OOO, Probability = 0.25

Would you like more details, or have any questions about these calculations?

Related Questions:

1. What is the probability of getting exactly two even numbers in three rolls?
2. How does changing the number of rolls affect the probability calculations for events like these?
3. If a fourth roll was added, how would you calculate the probability for events similar to A, B, or C?
4. What is the probability of rolling all even numbers (EEE) or all odd numbers (OOO) in three rolls?
5. How would probabilities change if the dice used had different properties (e.g., a biased dice)?

Tip:

When calculating probabilities for independent events, multiply the probabilities of each desired outcome per roll if you need the exact probability per outcome rather than counting favorable outcomes among a set.