Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that the sum of the rolls is 8?

Answer

To solve the problem of finding the probability that the sum of the rolls of two number cubes (dice) is 8, we can follow these steps:

### Step 1: Identify the total number of outcomes
When rolling two dice, each die has 6 faces. Therefore, the total number of possible outcomes when rolling two dice is:
\[ 6 \times 6 = 36 \]

### Step 2: Determine the favorable outcomes for a sum of 8
Next, we need to find all the combinations of the two dice that result in a sum of 8. The possible pairs (Die 1, Die 2) that give a sum of 8 are:
1. (2, 6)
2. (3, 5)
3. (4, 4)
4. (5, 3)
5. (6, 2)

Counting these combinations, we find there are 5 favorable outcomes.

### Step 3: Calculate the probability
The probability \( P \) of an event is given by the formula:
\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we found:
\[ P(\text{sum is 8}) = \frac{5}{36} \]

### Final Answer
Thus, the probability that the sum of the rolls is 8 is:
\[ \frac{5}{36} \]

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