dice probability question

This is a revision question for a phase test that i could sure use some help with!

A dice game consitsts of throwing 2 six sided dice and noting the score on them. If the score is greater than 9 or at least one dice shows a 6 then you score 3 points, otherwise you lose 1 point. Calculate the probability of gaining 3 points on a single throw. What is the average (or expected) number of points you will gain per throw.

i make the probability of scoreing 3 points as 12 over 36, but i don`t know how to do the rest.

any suggestions?

Cheers