You roll two dice. What is the probability that the sum of the dice is even and one die shows a 4? A 6x6 table of dice outcomes will help you to answer this question.

A. 1/6.

B. 5/18.

C. 2/3.

D. 5/36.

Out of the 36 possible entries in the 6x6 table, five have one or two 4's, and an even sum.

Die 1 Die 2
4. 2
4. 4
4. 6
2. 4
6. 4
Answer: 5/36

I have assumed that two fours meets the criteria

To find the probability that the sum of the dice is even and one die shows a 4, we need to determine the number of favorable outcomes and the total number of possible outcomes.

Let's first create a 6x6 table of all possible outcomes when rolling two dice:

| | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 4 | 5 | 6 | 7 | 8 | 9 |10|
| 5 | 6 | 7 | 8 | 9 |10|11|
| 6 | 7 | 8 | 9 |10|11|12|

In the table above, the numbers represent the sum of the two dice. We are interested in finding the outcomes where the sum is even and one die shows a 4.

Let's highlight the favorable outcomes:

| | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | | | | | | |
| 2 | | | | | | * |
| 3 | | | | | * | |
| 4 | | * | | | * | |
| 5 | | | | | | |
| 6 | | | | | | |

From the table, we can see that there are 5 favorable outcomes.

Now, let's determine the total number of possible outcomes. When rolling two dice, each die has 6 faces, so there are 6 possible outcomes for each die. Since we are rolling two dice, there are a total of 6 x 6 = 36 possible outcomes.

Therefore, the probability of the sum being even and one die showing a 4 is favorable outcomes / possible outcomes = 5/36.

Hence, the correct answer is option D. 5/36.