There are a number of ways to find the answer. Among them are
1. List the possible outcomes (all 36 of them), and count the ones that are even (18 of them). The resulting probability is 18/36 = 1/2.
2. Realize that half the numbers are even and half are odd on one die, so the sums will have these probabilities: (assuming fair dice)
p(odd, odd) = 1/4, result is divisible by 2
p(odd, even) = 1/4, result is not divisible by 2
p(even, odd) = 1/4, result is not divisible by 2
p(even, even) = 1/4, result is divisible by 2.
Thus, the probability that the result is divisible by 2 is (1/4) + (1/4) = 1/2
1. List the possible outcomes (all 36 of them), and count the ones that are even (18 of them). The resulting probability is 18/36 = 1/2.
2. Realize that half the numbers are even and half are odd on one die, so the sums will have these probabilities: (assuming fair dice)
p(odd, odd) = 1/4, result is divisible by 2
p(odd, even) = 1/4, result is not divisible by 2
p(even, odd) = 1/4, result is not divisible by 2
p(even, even) = 1/4, result is divisible by 2.
Thus, the probability that the result is divisible by 2 is (1/4) + (1/4) = 1/2