We want to find the probability of rolling a sum of 3 on the first roll and a sum of 4 on the second roll. Let's break this down:

Step 1: Understand the two events

• Event 1: Rolling a sum of 3. From the table, the probability of this is $\frac{2}{36}$.
• Event 2: Rolling a sum of 4. From the table, the probability of this is $\frac{3}{36}$.

Step 2: Analyze the relationship between the events

Rolling the dice twice involves independent events. The result of the first roll does not affect the result of the second roll. Therefore, the probabilities of the two events can be multiplied.

Step 3: Calculate the combined probability

The probability of both events happening is the product of their individual probabilities:

$P(\text{sum of 3 on first roll and sum of 4 on second roll}) = \frac{2}{36} \times \frac{3}{36}$

$P = \frac{6}{1296} = \frac{1}{216}$

Conclusion:

The probability of getting a sum of 3 on the first roll and a sum of 4 on the second roll is $\frac{1}{216}$.

Correct Answer:

The correct choice is C: The probability is $\frac{2}{36} \times \frac{3}{36}$ because the two events are independent.

Do you want more details or have any questions about this?

Here are five related questions:

1. What is the probability of rolling a sum of 5 on both rolls?
2. What is the probability of rolling a sum of 7 on the first roll and 11 on the second?
3. How would the probability change if the events were dependent?
4. Can you explain the "mutually exclusive" concept and how it differs from independence?
5. How would you calculate the probability of getting a sum of 12 on both rolls?

Tip: When calculating probabilities for independent events, always multiply their individual probabilities!