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