Two dice are rolled simultaneously. What is the probability of
getting prime number on second die?

Answer

To solve the problem of finding the probability of getting a prime number on the second die when two dice are rolled simultaneously, we can follow these steps:

### Step-by-Step Solution:

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

2. **Identify Prime Numbers**:
The prime numbers that can appear on a die are 2, 3, and 5. Thus, the prime numbers on the second die are:
\[ \text{Prime numbers} = \{2, 3, 5\} \]

3. **Count Favorable Outcomes**:
For each prime number on the second die, any number from 1 to 6 can appear on the first die. Therefore, we can calculate the favorable outcomes:
- If the second die shows 2, the first die can show: 1, 2, 3, 4, 5, or 6 (6 possibilities).
- If the second die shows 3, the first die can show: 1, 2, 3, 4, 5, or 6 (6 possibilities).
- If the second die shows 5, the first die can show: 1, 2, 3, 4, 5, or 6 (6 possibilities).

Thus, the total number of favorable outcomes is:
\[ \text{Favorable outcomes} = 6 + 6 + 6 = 18 \]

4. **Calculate the Probability**:
The probability \( P \) of getting a prime number on the second die is given by the ratio of the number of favorable outcomes to the total outcomes:
\[ P(\text{Prime on second die}) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{18}{36} = \frac{1}{2} \]

### Final Answer:
The probability of getting a prime number on the second die is:
\[ \frac{1}{2} \]