This problem involves rolling two dice and calculating the probability of obtaining a sum of 4.

Let's break it down:

Possible combinations of dice rolls that add up to 4:

• (1, 3)
• (2, 2)
• (3, 1)

These are the three possible outcomes where the sum is 4.

Total possible outcomes:

When rolling two dice, each die has 6 sides, so there are a total of $6 \times 6 = 36$ possible outcomes.

Probability:

The probability of rolling a sum of 4 is the number of favorable outcomes divided by the total number of possible outcomes. This is:

$P(\text{sum of 4}) = \frac{3}{36} = \frac{1}{12}$

Therefore, the correct answer is:

b) $\frac{1}{12}$

Would you like further details or have any questions on how to approach similar problems?

Here are some related questions:

1. What is the probability of rolling a sum of 7 with two dice?
2. How many possible outcomes result in a sum of 10?
3. If the dice are not fair (one die is biased), how would the probability change?
4. How do the probabilities change if you roll three dice instead of two?
5. What is the probability of rolling a sum of 2 or 12?

Tip: When dealing with dice probability problems, always remember to count both the favorable outcomes and the total possible outcomes, and express the result as a fraction for clarity.