Two dice are thrown at a time, find the probability that the sum of the numbers on the upper faces of the dice is equal to 3.

Answer

To solve the problem of finding the probability that the sum of the numbers on the upper faces of two thrown dice equals 3, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Total Number of Outcomes:**
When two dice are thrown, each die has 6 faces. Therefore, the total number of outcomes when throwing two dice is calculated as:
\[ \text{Total Outcomes} = 6 \times 6 = 36 \]

2. **Identify the Favorable Outcomes:**
We need to find the combinations of the numbers on the two dice that sum up to 3. The possible combinations are:
- Die 1 shows 1 and Die 2 shows 2 (1, 2)
- Die 1 shows 2 and Die 2 shows 1 (2, 1)

Thus, the favorable outcomes that give a sum of 3 are:
- (1, 2)
- (2, 1)

Therefore, the number of favorable outcomes is:
\[ \text{Favorable Outcomes} = 2 \]

3. **Calculate the Probability:**
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes. Thus, the probability \( P \) that the sum of the numbers on the upper faces of the dice equals 3 is:
\[ P(\text{sum} = 3) = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{2}{36} \]

4. **Simplify the Probability:**
We can simplify the fraction:
\[ P(\text{sum} = 3) = \frac{2}{36} = \frac{1}{18} \]

### Final Answer:
The probability that the sum of the numbers on the upper faces of the dice is equal to 3 is:
\[ \frac{1}{18} \]