12. A fair die is tossed once. What is the sample space for the event of rolling a prime number? A. $$ \{1,3,5\} $$ B. $$ \{2,4,6\} $$ C. $$ \{2,3,5\} $$ D $$ \{1,2,3,4,5,6\} $$

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To determine the sample space for the event of rolling a prime number when a fair die is tossed once, we first need to identify the prime numbers within the range of possible outcomes from rolling a die.

1. **Identify the possible outcomes when rolling a die:**
   The possible outcomes when rolling a fair six-sided die are $$ \{1, 2, 3, 4, 5, 6\} $$.

2. **Identify the prime numbers within this range:**
   A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. The prime numbers from 1 to 6 are:
   - 2 (divisors: 1, 2)
   - 3 (divisors: 1, 3)
   - 5 (divisors: 1, 5)

The numbers 1, 4, and 6 are not prime:
   - 1 is not prime (it has only one divisor).
   - 4 is not prime (divisors: 1, 2, 4).
   - 6 is not prime (divisors: 1, 2, 3, 6).

3. **Construct the sample space for rolling a prime number:**
   The prime numbers from the outcomes of the die are $$ \{2, 3, 5\} $$.

Thus, the sample space for the event of rolling a prime number is $$ \{2, 3, 5\} $$.

The correct answer is:
C. $$ \{2, 3, 5\} $$
The sample space for rolling a prime number is $$ \{2, 3, 5\} $$.

12. A fair die is tossed once. What is the sample space for the event of rolling a prime number? A. \( \{1,3,5\} \) B. \( \{2,4,6\} \) C. \( \{2,3,5\} \) D \( \{1,2,3,4,5,6\} \)

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