The question in the image asks: "If two dice are thrown, what is the probability that the sum is even?"

Let's solve this step by step:

1. Total Outcomes

When two dice are thrown, each die has 6 faces. Therefore, the total number of possible outcomes is:

$6 \times 6 = 36$

2. Favorable Outcomes

To get an even sum, the sum of the numbers on both dice must be even. This happens in the following cases:

• Both numbers are even (even + even = even).
• Both numbers are odd (odd + odd = even).

Even-Even combinations:

• (2, 2), (2, 4), (2, 6)
• (4, 2), (4, 4), (4, 6)
• (6, 2), (6, 4), (6, 6)

There are $3 \times 3 = 9$ even-even combinations.

Odd-Odd combinations:

• (1, 1), (1, 3), (1, 5)
• (3, 1), (3, 3), (3, 5)
• (5, 1), (5, 3), (5, 5)

There are $3 \times 3 = 9$ odd-odd combinations.

3. Total Even Sum Combinations

The total number of favorable outcomes where the sum is even is $9 + 9 = 18$.

4. Probability Calculation

The probability of getting an even sum is the number of favorable outcomes divided by the total number of outcomes:

$\frac{18}{36} = \frac{1}{2}$

Answer:

The correct option is (D) 1/2.

Would you like further details on any step, or do you have other questions?

Here are 5 related questions to explore:

1. What is the probability of getting an odd sum when two dice are rolled?
2. How do we calculate the probability of getting a specific sum when rolling two dice?
3. If three dice are rolled, what is the probability of getting an even sum?
4. How many possible outcomes are there when rolling two dice where the sum is greater than 7?
5. How would the calculation change if we were rolling two dice with a different number of faces?

Tip: Always start by determining the total number of possible outcomes before finding favorable outcomes to simplify probability problems.