Probability of getting an even sum when rolling a die twice:

To solve this problem, we need to determine the number of favorable outcomes and the total number of possible outcomes.

Step 1: Determine the total number of possible outcomes

When rolling a die twice, the total number of possible outcomes is found by multiplying the number of outcomes for each roll. Since a die has 6 sides, there are 6 outcomes for each roll.

So, the total number of possible outcomes = 6 * 6 = 36.

Step 2: Determine the number of favorable outcomes

To find the number of favorable outcomes, we need to consider all the possible combinations of outcomes that result in an even sum.

To simplify this, let's list all the possible outcomes for the first roll and the second roll:

Possible outcomes for the first roll: 1, 2, 3, 4, 5, 6
Possible outcomes for the second roll: 1, 2, 3, 4, 5, 6

Now, let's consider all the possible combinations of outcomes:

1 + 1 = 2 (even)
1 + 2 = 3 (odd)
1 + 3 = 4 (even)
1 + 4 = 5 (odd)
1 + 5 = 6 (even)
1 + 6 = 7 (odd)
2 + 1 = 3 (odd)
2 + 2 = 4 (even)
2 + 3 = 5 (odd)
2 + 4 = 6 (even)
2 + 5 = 7 (odd)
2 + 6 = 8 (even)
3 + 1 = 4 (even)
3 + 2 = 5 (odd)
3 + 3 = 6 (even)
3 + 4 = 7 (odd)
3 + 5 = 8 (even)
3 + 6 = 9 (odd)
4 + 1 = 5 (odd)
4 + 2 = 6 (even)
4 + 3 = 7 (odd)
4 + 4 = 8 (even)
4 + 5 = 9 (odd)
4 + 6 = 10 (even)
5 + 1 = 6 (even)
5 + 2 = 7 (odd)
5 + 3 = 8 (even)
5 + 4 = 9 (odd)
5 + 5 = 10 (even)
5 + 6 = 11 (odd)
6 + 1 = 7 (odd)
6 + 2 = 8 (even)
6 + 3 = 9 (odd)
6 + 4 = 10 (even)
6 + 5 = 11 (odd)
6 + 6 = 12 (even)

From the above list, we can see that there are 18 favorable outcomes (outcomes that result in an even sum).

Step 3: Calculate the probability

The probability of getting an even sum is given by the number of favorable outcomes divided by the total number of possible outcomes.

Therefore, the probability = favorable outcomes / total outcomes = 18 / 36 = 1/2.

Hence, the correct answer is option 'C' - 1/2.