To find the probability of rolling two number cubes (dice) and getting a sum of 6 or 11, we first need to calculate the probabilities of each of these sums separately and then combine them.
Step 1: Calculate the total possible outcomes when rolling two dice.
- There are \(6\) faces on each die, so the total number of outcomes when rolling two dice is \(6 \times 6 = 36\).
Step 2: Determine the number of outcomes for each sum.
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Sum of 6: The combinations that give a sum of 6 are:
- (1, 5)
- (2, 4)
- (3, 3)
- (4, 2)
- (5, 1)
This gives us a total of 5 combinations for a sum of 6. Therefore, the probability of a sum of 6 is: \[ \frac{5}{36} \]
-
Sum of 11: The combinations that give a sum of 11 are:
- (5, 6)
- (6, 5)
This gives us a total of 2 combinations for a sum of 11. Therefore, the probability of a sum of 11 is: \[ \frac{2}{36} = \frac{1}{18} \]
Step 3: Combine the probabilities for sums of 6 and 11. The total probability of getting a sum of 6 or 11 is the sum of the individual probabilities: \[ P(6 \text{ or } 11) = P(6) + P(11) = \frac{5}{36} + \frac{2}{36} = \frac{7}{36} \]
Now we evaluate the answer choices based on this calculation:
- \( \frac{5}{36} \cdot \frac{2}{36} \) - This is a multiplication of probabilities, which is incorrect.
- \( \frac{6}{36} \cdot \frac{2}{36} \) - This is also incorrect.
- \( \frac{6}{36} + \frac{2}{36} \) - This is incorrect since \( \frac{6}{36} \) is not the correct probability for a sum of 6.
- \( \frac{5}{36} + \frac{2}{36} \) - This matches our calculation for the sum probs, but this option is not listed correctly.
None of the options provided in the responses accurately reflect the addition of \( \frac{5}{36} + \frac{2}{36} \).
However, based on the closest patterns, if discussed in fundamentals, the correct calculation should be represented by: \( \frac{5}{36} + \frac{2}{36} \), which isn't explicitly there, but if you had to choose, the one that shows addition would be the most aligned: \( \frac{6}{36} + \frac{2}{36} \) if viewed simply as a structure.
So, choose accordingly based on the sum basics mentioned here.