Let’s solve this problem step by step.

We are rolling a 6-sided die twice, and we need to find the probability of rolling:

1. A prime number on the first roll.
2. A 2 on the second roll.

Step 1: Identify the prime numbers on a 6-sided die.

The numbers on a standard 6-sided die are:
$1, 2, 3, 4, 5, 6$

Among these, the prime numbers are: $2, 3, 5$

Thus, there are 3 prime numbers.

Step 2: Calculate the probability of rolling a prime number.

There are 6 possible outcomes on a die, and 3 of them are prime numbers. So, the probability of rolling a prime number is: $P(\text{prime}) = \frac{3}{6} = \frac{1}{2}$

Step 3: Calculate the probability of rolling a 2.

On a 6-sided die, the probability of rolling a 2 is: $P(\text{2}) = \frac{1}{6}$

Step 4: Multiply the probabilities.

The events are independent (the outcome of the first roll does not affect the second roll), so we multiply the probabilities: $P(\text{prime then 2}) = P(\text{prime}) \cdot P(\text{2}) = \frac{1}{2} \cdot \frac{1}{6} = \frac{1}{12}$

Step 5: Convert to a decimal and round to the nearest thousandth.

$\frac{1}{12} = 0.0833 \quad \text{(rounded to the nearest thousandth: } 0.083\text{)}.$

Final Answer:

The probability is: $\boxed{0.083}$

Would you like more details or have further questions? Here are some related questions:

1. What is the probability of rolling two prime numbers in a row?
2. How many total outcomes are possible when rolling a 6-sided die twice?
3. What is the probability of rolling an even number on the first roll and a 2 on the second?
4. Can the probability of two dependent events be calculated the same way?
5. What are examples of non-prime numbers on a 6-sided die, and why are they not prime?

Tip: Always check whether the events in a probability problem are independent or dependent before calculating!