What is the probability of getting either a sum of 66 or at least one 66 in the roll of a pair of dice?

So I'm hoping you mean 6, or else the probability is 0. So the possible ways of getting a sum of 6 is 1&5, 2&4, 3&3, 4&2, 5&1. There are 36 different ways of rolling the dice, so divide the 5 possible ways by 36. Then, we need to add the possibility of getting at least one 6 in the roll. It doesn't matter what the other die is, so for each die, the probability is 1/6, and for both, the probability is 2/6. Add this to the probability of getting a sum of 6, and you get your answer.