The image you uploaded asks for the probability that the sum of the numbers on two dice is even.

To find this, consider the following:

• Each die has 6 faces with numbers 1 through 6.
• For two dice, there are a total of $6 \times 6 = 36$ possible outcomes.
• The sum is even if both dice show either an odd number or an even number.

Number of ways for both dice to show odd numbers (odd + odd = even):

• Odd numbers on a die: 1, 3, 5
• There are 3 choices for the first die and 3 choices for the second die, giving $3 \times 3 = 9$ combinations.

Number of ways for both dice to show even numbers (even + even = even):

• Even numbers on a die: 2, 4, 6
• Similarly, there are $3 \times 3 = 9$ combinations for this case.

Adding both scenarios, the number of favorable outcomes is $9 + 9 = 18$.

Thus, the probability that the sum is even is: $\frac{18}{36} = \frac{1}{2}$

Would you like more details on any specific part of this explanation?

Related questions you might find interesting:

1. What is the probability that the sum is odd when two dice are thrown?
2. Can you explain how to calculate the probability of a specific sum, like 7 or 8?
3. How does the distribution of sums vary when more than two dice are used?
4. What are the most and least common sums with two dice?
5. How can understanding dice probabilities help in games like Monopoly or other board games?

Tip: When analyzing dice probabilities, considering symmetry (like even vs odd outcomes) can simplify calculations significantly.