To find the probability of a sum of 6 given that the roll is a "double", we first need to determine the probability of getting a double.
Since there are 6 possible outcomes for each dice roll (1, 2, 3, 4, 5, 6), the total number of possible outcomes when rolling two dice is 6 x 6 = 36.
Next, we need to find the number of ways to get a double.
There are 6 possible doubles: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), and (6, 6).
So the probability of getting a double is 6/36, which can be simplified to 1/6.
Now, given that the roll is a double, we need to find the probability of the sum being 6.
Out of the 6 possible doubles, only two of them add up to a sum of 6: (1, 5) and (5, 1).
Therefore, the probability of a sum of 6 given that the roll is a double is 2/6, which simplifies to 1/3.