(a)
There are a total of 6 * 6 = 36 possible outcomes when rolling a pair of dice. Out of those, there are 6 outcomes where doubles are rolled (1-1, 2-2, 3-3, 4-4, 5-5, 6-6).
So, the probability of rolling doubles is 6/36 = 1/6.
(b)
Out of the 36 possible outcomes, there are 3 ways to get a sum of 10 and doubles rolled (4-6, 5-5, 6-4).
So, the probability of getting a sum of 10 and doubles rolled is 3/36 = 1/12.
(c)
Since we are given that doubles are rolled, the only possible outcomes are the 6 doubles mentioned in part (a). Out of these, only 1 doubles pair (5-5) has a sum of 10.
So, the probability of getting a sum of 10, given that doubles are rolled, is 1/6.