Question

Find the probability of rolling a sum of 6 or 11 when rolling two number cubes. Enter your response as a fraction.

Answer 1

To find the probability of rolling a sum of 6 or 11 with two number cubes (dice), we first need to determine the total number of possible outcomes when rolling the dice.

Each die has 6 faces, so the total number of possible outcomes when rolling two dice is:

\[
6 \times 6 = 36
\]

Next, we will find the number of ways to achieve a sum of 6 and a sum of 11.

### Sum of 6
The combinations of dice that yield a sum of 6 are:
- (1, 5)
- (2, 4)
- (3, 3)
- (4, 2)
- (5, 1)

Counting these combinations, we have 5 outcomes that result in a sum of 6.

### Sum of 11
The combinations of dice that yield a sum of 11 are:
- (5, 6)
- (6, 5)

Counting these combinations, we have 2 outcomes that result in a sum of 11.

### Total Successful Outcomes
Now we add the successful outcomes for both sums:
- Sum of 6: 5 outcomes
- Sum of 11: 2 outcomes

Total successful outcomes = \( 5 + 2 = 7 \)

### Probability
Now we can calculate the probability of rolling a sum of 6 or 11:

\[
\text{Probability} = \frac{\text{Number of successful outcomes}}{\text{Total number of outcomes}} = \frac{7}{36}
\]

Thus, the probability of rolling a sum of 6 or 11 when rolling two number cubes is:

\[
\boxed{\frac{7}{36}}
\]