Two dice are thrown together and the two numbers are added. What is the probability that the total is a prime number?

Possible totals run from 2 to 12; the prime totals are 2, 3, 5, 7 and 11. Their counts out of 36 are 1, 2, 4, 6 and 2, adding to 15. $P=\frac{15}{36}=\frac{5}{12}.\frac{7}{18}=\frac{14}{36}$ leaves out the total 2; $\frac{1}{2}$ guesses that half the outcomes work; $\frac{5}{36}$ counts just one of the five totals.