We roll two fair 6-sided dice. Each one of the 36 possible outcomes is assumed to be equally likely.
(a) Find the probability that doubles are rolled.
(b) Given that the roll results in a sum of 4 or less, find the conditional probability that doubles are rolled.
(c) Find the probability that at least one die roll is a 6.
(d) Given that the two dice land on different numbers, find the conditional probability that at least one die roll is a 6.