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In rolling two fair dice, the probability of obtaining a sum greater than 10 is 3 in 36 or 1 in 12, and the probability of obtaining a sum divisible by 6 is 6 in 36 or 1 in 6. Since the two probabilities come from the same population of 36 possible outcomes, the combined probability is the inclusive or of the two result sets, 8 in 36 or 2 in 9.

The results that match the sum>10 target are 5-6, 6-5, and 6-6.

The results that match the divisibility by 6 target are 1-5, 2-4, 3-3, 4-2, 5-1, and 6-6.

The results that match the combined target are 1-5, 2-4, 3-3, 4-2, 5-1, 5-6, 6-5, and 6-6.

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Q: In rolling two fair dice what is the probability of obtaining a sum greater than 10 or a sum divisible by 6?
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