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

Answer

To solve the problem of finding the probability of getting a prime number on each die when rolling two dice, we can follow these steps:

### Step 1: Identify the possible outcomes
When rolling two dice, each die has 6 faces numbered from 1 to 6. Therefore, the total number of outcomes when rolling two dice is:
\[ 6 \times 6 = 36 \]

### Step 2: Identify the prime numbers on a die
The prime numbers between 1 and 6 are:
- 2
- 3
- 5

Thus, the prime numbers on a die are 2, 3, and 5.

### Step 3: Determine the favorable outcomes
We need to find all the combinations where both dice show prime numbers. The prime numbers available are 2, 3, and 5. We can list the combinations:

1. (2, 2)
2. (2, 3)
3. (2, 5)
4. (3, 2)
5. (3, 3)
6. (3, 5)
7. (5, 2)
8. (5, 3)
9. (5, 5)

Counting these combinations, we find there are a total of 9 favorable outcomes.

### Step 4: Calculate the probability
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we found:
\[ \text{Probability} = \frac{9}{36} = \frac{1}{4} \]

### Conclusion
Thus, the probability of getting a prime number on each die when rolling two dice is:
\[ \frac{1}{4} \]

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