A die is rolled. List the outcomes of the event A if:
A is the event that a prime number appears.

Answer

To solve the problem, we need to identify the outcomes of the event A, where A is defined as the event that a prime number appears when a die is rolled.

### Step-by-Step Solution:

1. **Identify the possible outcomes when a die is rolled.**
- A standard die has six faces, numbered from 1 to 6. Therefore, the possible outcomes are:
\[ \{1, 2, 3, 4, 5, 6\} \]

2. **Define what a prime number is.**
- A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, a prime number can only be divided evenly (without a remainder) by 1 and the number itself.

3. **List the prime numbers between 1 and 6.**
- Now, we will check which of the numbers from the outcomes (1 to 6) are prime:
- **1**: Not a prime number (only divisible by 1).
- **2**: Prime number (divisible by 1 and 2).
- **3**: Prime number (divisible by 1 and 3).
- **4**: Not a prime number (divisible by 1, 2, and 4).
- **5**: Prime number (divisible by 1 and 5).
- **6**: Not a prime number (divisible by 1, 2, 3, and 6).

4. **List the prime numbers identified.**
- From the above checks, the prime numbers that appear when a die is rolled are:
\[ \{2, 3, 5\} \]

5. **State the outcomes of event A.**
- Therefore, the outcomes of event A, where a prime number appears when a die is rolled, are:
\[ A = \{2, 3, 5\} \]

### Final Answer:
The outcomes of the event A (where a prime number appears) are \( \{2, 3, 5\} \).