To determine the probability of rolling two number cubes (dice) and getting a sum of 6 or 11, we need to consider the possible outcomes for each sum.
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Finding the probability of getting a sum of 6: The pairs that result in a sum of 6 are:
- (1, 5)
- (2, 4)
- (3, 3)
- (4, 2)
- (5, 1)
There are 5 outcomes that yield a sum of 6.
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Finding the probability of getting a sum of 11: The pairs that result in a sum of 11 are:
- (5, 6)
- (6, 5)
There are 2 outcomes that yield a sum of 11.
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Total outcomes: When rolling two dice, there are a total of 6 sides on the first die and 6 sides on the second die, which gives us \(6 \times 6 = 36\) possible outcomes.
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Calculating the probabilities:
- The probability of getting a sum of 6 is \( \frac{5}{36} \).
- The probability of getting a sum of 11 is \( \frac{2}{36} \).
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Combining the probabilities: Since the events are mutually exclusive (you can't roll a sum of 6 and 11 at the same time), we can add the probabilities: \[ P(6 \text{ or } 11) = P(6) + P(11) = \frac{5}{36} + \frac{2}{36} = \frac{7}{36} \]
Based on this information, the correct calculation for finding the probability of rolling two dice and getting a sum of 6 or 11 is represented by: \[ \frac{5}{36} + \frac{2}{36} \]
Thus, the first option: \[ \frac{5}{36} + \frac{2}{36} \] is the correct response.