To find the probability that the sum of two rolled numbers is even, we need to determine the number of favorable outcomes (sums that are even) and divide it by the total number of possible outcomes.
Let's consider all possible outcomes when two numbers are rolled on a fair, six-sided die:
The possible outcomes for rolling the first number are 1, 2, 3, 4, 5, and 6. For each of these outcomes, the second number could also be any of these six values.
To determine the total number of possible outcomes, we multiply the number of possibilities for the first roll (6) by the number of possibilities for the second roll (also 6). So, there are a total of 6 * 6 = 36 possible outcomes.
Now, let's consider the favorable outcomes: sums that are even. To get an even number, we can have:
- An even number for the first roll and an even number for the second roll: There are three even numbers (2, 4, and 6). Since there are six choices for each roll, there are 3 * 3 = 9 favorable outcomes in this case.
- An odd number for the first roll and an odd number for the second roll: There are three odd numbers (1, 3, and 5). Again, there are 3 * 3 = 9 favorable outcomes in this case.
Adding the favorable outcomes from both cases, we have a total of 9 + 9 = 18 favorable outcomes.
Finally, to find the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
P(sum is even) = favorable outcomes / total outcomes = 18 / 36 = 1/2
Therefore, the correct answer is C. one-half.