Rolling two dice, what is the probability of getting 6 on either of them, but not both? Rolling two dice, what is the probability of getting 6 on one of them, but not both?

Label the dice 1 and 2. You want to find the probability that die 1 rolls a six ($p = \frac 16$) while die 2 rolls anything else ($p = \frac 56$) OR vice versa.
The first case is simply $p = \frac 16 \cdot \frac 56 = \frac {5}{36} $.
The second case is simply the mirror of the first, with the same probability. 
So the final probability is $p = (2)(\frac{5}{36}) = \frac {5}{18}$
