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:
- (1,5)
- (2,4)
- (3,3)
- (4,2)
- (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:
- (5,6)
- (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. \( \frac{5}{36} + \frac{2}{36} \)