In how many ways can two dice be rolled to yield a sum divisible by 3?

To find out how many ways two dice can be rolled to yield a sum divisible by 3, we need to consider all the possible outcomes when rolling two dice and check which sums are divisible by 3.

There are 6 possible outcomes for each of the two dice, resulting in a total of 6 * 6 = 36 possible combinations when rolling two dice.

Next, we list the sums for each possible combination:

Dice 1: 1, 2, 3, 4, 5, 6
Dice 2: 1, 2, 3, 4, 5, 6

Sum: 2, 3, 4, 5, 6, 7
3, 4, 5, 6, 7, 8
4, 5, 6, 7, 8, 9
5, 6, 7, 8, 9, 10
6, 7, 8, 9, 10, 11
7, 8, 9, 10, 11, 12

From this list, we can see that the sums divisible by 3 are:
3, 6, 9, 12

There are a total of 4 possible sums.

Therefore, there are 4 ways two dice can be rolled to yield a sum divisible by 3.