To find the probability of rolling a sum of 6 or 11 when rolling two six-sided number cubes (dice), we first need to determine the total number of possible outcomes and the number of successful outcomes for each sum.
Total Possible Outcomes: When rolling two dice, each die has 6 sides, so the total number of possible outcomes when rolling two dice is:
\[ 6 \times 6 = 36 \]
Successful Outcomes for a Sum of 6: The combinations that yield a sum of 6 are:
- (1, 5)
- (2, 4)
- (3, 3)
- (4, 2)
- (5, 1)
This gives us a total of 5 successful outcomes for a sum of 6.
Successful Outcomes for a Sum of 11: The combinations that yield a sum of 11 are:
- (5, 6)
- (6, 5)
This gives us a total of 2 successful outcomes for a sum of 11.
Total Successful Outcomes: Adding the successful outcomes from both sums:
\[ 5 \text{ (for sum of 6)} + 2 \text{ (for sum of 11)} = 7 \]
Calculating the Probability: The probability of rolling a sum of 6 or 11 is then given by the number of successful outcomes divided by the total number of possible outcomes:
\[ P(\text{sum of 6 or 11}) = \frac{\text{Number of successful outcomes}}{\text{Total outcomes}} = \frac{7}{36} \]
Thus, the probability of rolling a sum of 6 or 11 when rolling two number cubes is:
\[ \frac{7}{36} \]