If two 6-sided dice are thrown, what is the probability that the sum of the faces equals 3 ? A. \(1 / 6\) B. \(1 / 9\) C. \(1 / 18\) D. \(1 / 24\) E. \(1 / 36\)

When we talk about a 6-sided die, we are referring to a cube with faces numbered from 1 to 6. Each face has an equal likelihood of landing face-up when the die is rolled. This makes understanding dice a fundamental concept in probability.
Rolling a single die has 6 possible outcomes since any one of the six faces can land face-up. The probability of rolling any specific number, such as a 3, is therefore \(\frac{1}{6}\).
When rolling two 6-sided dice, the complexity and number of outcomes increase. For two dice, you need to consider every possible combination of numbers that the two dice could show. This results in \(\text{6 faces per die} \times \text{6 faces per die} = 36 \text{ total possible outcomes}\). This is why it's important to calculate total possible outcomes before moving to more complex probability calculations.

When solving problems involving the sum of the faces of two dice, it's useful to list out all potential outcomes.
For instance, if the problem asks for the sum of the faces to equal a certain number, say 3, you need to identify all the pairs that can achieve this.
In this exercise, the pairs of dice faces that add up to 3 are (1, 2) and (2, 1). Therefore, there are exactly 2 favorable outcomes. Identifying these favorable outcomes is crucial before calculating the actual probability.

Calculating the probability follows a few straightforward steps:

• Step 1: Understand the problem to ensure you know what is being asked. For instance, here we need the sum of the faces to be 3.


• Step 2: Determine the total possible outcomes. For two 6-sided dice, this would be 36.


• Step 3: Identify the favorable outcomes. As we learned, the combinations (1, 2) and (2, 1) give us a sum of 3, making 2 favorable outcomes.


• Step 4: Calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes, which is \(\frac{2}{36} = \frac{1}{18}\).

This method can be used to solve various probability problems involving dice, making sure you apply the same logical steps each time.