Final answer:
The probability of rolling a sum greater than five with two dice is 31/36, which does not match any of the given answer options suggesting an error in the provided choices.
Step-by-step explanation:
To find the probability that the sum of two rolls of a die is greater than five, we first consider the sample space and the favorable outcomes. A six-sided die has the numbers {1, 2, 3, 4, 5, 6}, so when rolling twice, there are 6 x 6 = 36 possible outcomes. To have a sum greater than five, we need to consider pairs such as (1,5), (2,4), (3,3), and so forth. We exclude pairs where both values are 1, 2, or 1 and 2, like (1,1), (1,2), or (2,2), which make up 5 of the 36 total outcomes. So, we have 36 - 5 = 31 possible outcomes that have a sum over five.
The probability of the sum being greater than five is thus 31 favorable outcomes divided by 36 possible outcomes, which simplifies to 31/36. This is not among the options provided, indicating a possible error in the question or answer choices. None of the provided options (a) 5/12, (b) 7/12, (c) 1/4, or (d) 1/6 are correct based on the calculation.