To find the probability of rolling two number cubes (two six-sided dice) and getting a sum of either 6 or 11, follow these steps:
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Calculate the total number of possible outcomes when rolling two dice: Each die has 6 faces, so the total number of outcomes when rolling two dice is: \[ 6 \times 6 = 36 \]
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Calculate the number of ways to get a sum of 6: The combinations that result in a sum of 6 are:
- (1, 5)
- (2, 4)
- (3, 3)
- (4, 2)
- (5, 1)
There are a total of 5 combinations that give you a sum of 6.
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Calculate the number of ways to get a sum of 11: The combinations that result in a sum of 11 are:
- (5, 6)
- (6, 5)
There are a total of 2 combinations that give you a sum of 11.
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Combine the results: The total number of combinations that give you a sum of 6 or 11 is: \[ 5 \text{ (for 6)} + 2 \text{ (for 11)} = 7 \text{ combinations} \]
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Calculate the probability: The probability of rolling a sum of 6 or 11 is given by the ratio of favorable outcomes to total outcomes: \[ P(\text{sum of 6 or 11}) = \frac{\text{Number of combinations for 6 or 11}}{\text{Total outcomes}} = \frac{7}{36} \]
Final Answer: The correct calculation shows that the probability of rolling a sum of 6 or 11 when rolling two number cubes is: \[ \frac{7}{36} \]
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