Final answer:
The probability that the sum of the numbers on two dice is six or twelve is 1/6, or approximately 0.166667 when expressed as a decimal.
Step-by-step explanation:
The question concerns the probability of rolling two dice and getting a sum of either six or twelve. To calculate this, we need to consider all of the possible outcomes when two dice are rolled and then identify which outcomes give us the sums in question. There are 36 possible outcomes when rolling two dice (6 sides on the first die × 6 sides on the second die).
To get a sum of six, the following combinations are possible: (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1). That is 5 possible outcomes. To get a sum of twelve, there is only one combination: (6, 6), which is 1 possible outcome. So, the total number of desired outcomes is 5 + 1 = 6.
Therefore, the probability of rolling a sum of six or twelve is 6 out of 36 outcomes, which simplifies to 1 out of 6. As a fraction in lowest terms, this is 1/6, or as a decimal rounded to the nearest millionth, it is approximately 0.166667.