To solve this problem, we first need to determine the total number of possible outcomes when rolling two dice. Since each die has six possible outcomes (1, 2, 3, 4, 5, or 6), there are 6 x 6 = 36 possible outcomes when rolling two dice.
Next, we need to determine the number of outcomes where the sum of the two dice is less than 6. These outcomes are:
Rolling a 1 on the first die and a 1, 2, or 3 on the second die (3 outcomes)
Rolling a 2 on the first die and a 1 or 2 on the second die (2 outcomes)
Rolling a 3 on the first die and a 1 on the second die (1 outcome)
Therefore, there are a total of 3 + 2 + 1 = 6 outcomes where the sum of the two dice is less than 6.
Now we need to determine the number of outcomes where doubles are rolled among these 6 outcomes. Since doubles can only be rolled if both dice show the same number, there are only 3 possible outcomes where doubles are rolled: (1,1), (2,2), and (3,3).
Therefore, the probability of rolling doubles given that the sum on the two dice is less than 6 is 3/6 or 1/2.