Question

Which of the following shows the correct calculation for finding the probability of rolling two number cubes and getting a sum of 6 or 11?

Answer 1

To find the probability of rolling two number cubes (two six-sided dice) and getting a sum of either 6 or 11, follow these steps:

1. **Calculate the total number of possible outcomes when rolling two dice:**
Each die has 6 faces, so the total number of outcomes when rolling two dice is:
\[
6 \times 6 = 36
\]

2. **Calculate the number of ways to get a sum of 6:**
The combinations that result in a sum of 6 are:
- (1, 5)
- (2, 4)
- (3, 3)
- (4, 2)
- (5, 1)

There are a total of **5 combinations** that give you a sum of 6.

3. **Calculate the number of ways to get a sum of 11:**
The combinations that result in a sum of 11 are:
- (5, 6)
- (6, 5)

There are a total of **2 combinations** that give you a sum of 11.

4. **Combine the results:**
The total number of combinations that give you a sum of 6 or 11 is:
\[
5 \text{ (for 6)} + 2 \text{ (for 11)} = 7 \text{ combinations}
\]

5. **Calculate the probability:**
The probability of rolling a sum of 6 or 11 is given by the ratio of favorable outcomes to total outcomes:
\[
P(\text{sum of 6 or 11}) = \frac{\text{Number of combinations for 6 or 11}}{\text{Total outcomes}} = \frac{7}{36}
\]

**Final Answer:**
The correct calculation shows that the probability of rolling a sum of 6 or 11 when rolling two number cubes is:
\[
\frac{7}{36}
\]