We roll two fair 6-sided dice. Each one of the 36 possible outcomes is assumed to be equally likely. 1) Find the probability that doubles (i. e., having an equal number on the two dice) were rolled.
2) Given that the roll resulted in a sum of 4 or less, find the conditional probability that doubles were rolled.
3) Given that the two dice land on different numbers, find the conditional probability that at least one die is a 1.
4) Find the probability that at least one die is a 6.