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?

A. 5/36 + 2/36
B. 6/36 ⋅ 2/36
C. 5/36 ⋅ 2/36
D. 6/36 + 2/36

Answer 1

To find the probability of rolling two number cubes (dice) and getting a sum of 6 or 11, we first need to determine the total number of successful outcomes for each sum.

### Outcomes for a sum of 6:
The pairs that result in a sum of 6 are:
1. (1,5)
2. (2,4)
3. (3,3)
4. (4,2)
5. (5,1)

This gives us 5 successful outcomes for a sum of 6.

### Outcomes for a sum of 11:
The pairs that result in a sum of 11 are:
1. (5,6)
2. (6,5)

This gives us 2 successful outcomes for a sum of 11.

### Total Successful Outcomes for Both Sums:
- Successful outcomes for sum of 6 = 5
- Successful outcomes for sum of 11 = 2
- Total successful outcomes = 5 + 2 = 7

### Total Possible Outcomes:
When rolling two dice, the total number of possible outcomes is \(6 \times 6 = 36\).

### Probability Calculation:
The probability of rolling a sum of 6 or 11 is therefore:
\[
P(6 \text{ or } 11) = \frac{\text{Total successful outcomes}}{\text{Total possible outcomes}} = \frac{7}{36}
\]

Now, looking at the options provided:

A. \( \frac{5}{36} + \frac{2}{36} \) = \( \frac{7}{36} \) (correct)

B. \( \frac{6}{36} \cdot \frac{2}{36} \) (incorrect approach, not how we combine probabilities for sums)

C. \( \frac{5}{36} \cdot \frac{2}{36} \) (incorrect approach)

D. \( \frac{6}{36} + \frac{2}{36} \) = \( \frac{8}{36} \) (incorrect)

Thus, the correct calculation for the probability of rolling two number cubes and getting a sum of 6 or 11 is:

**A. \( \frac{5}{36} + \frac{2}{36} \)**