A dice is rolled two times or two dice are rolled together. Find the probability of getting:
an even number on each dice.

Answer

To find the probability of getting an even number on each die when a die is rolled two times (or two dice are rolled together), we can follow these steps:

### Step 1: Identify the total outcomes
When rolling two dice, each die has 6 faces. Therefore, the total number of outcomes when rolling two dice is:
\[ \text{Total Outcomes} = 6 \times 6 = 36 \]

### Step 2: Identify the favorable outcomes
The even numbers on a standard die are 2, 4, and 6. Thus, for each die, there are 3 even numbers.

When rolling two dice, we need both dice to show an even number. The favorable outcomes can be calculated as follows:
- For the first die, there are 3 choices (2, 4, or 6).
- For the second die, there are also 3 choices (2, 4, or 6).

Thus, the total number of favorable outcomes is:
\[ \text{Favorable Outcomes} = 3 \times 3 = 9 \]

### Step 3: Calculate the probability
The probability of getting an even number on each die is given by the ratio of the number of favorable outcomes to the total number of outcomes:
\[ \text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{9}{36} \]

### Step 4: Simplify the probability
Now, we can simplify the fraction:
\[ \frac{9}{36} = \frac{1}{4} \]

### Final Answer
The probability of getting an even number on each die is:
\[ \frac{1}{4} \]

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