A die is thrown 260 times. Prime numbers appear on the upper face 39 times. If a dia is thrown at random, what is the probability of getting a prime number?

Answer

To solve the problem of finding the probability of getting a prime number when a die is thrown, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Trials**:
- A die is thrown 260 times. This means the total number of possible outcomes (n of s) is 260.

2. **Identify the Number of Favorable Outcomes**:
- Prime numbers on a die are 2, 3, and 5. According to the problem, prime numbers appeared on the upper face 39 times. This means the number of favorable outcomes (n of e) is 39.

3. **Use the Probability Formula**:
- The probability of an event is given by the formula:
\[ P(E) = \frac{n(E)}{n(S)} \]
- Here, \( P(E) \) is the probability of getting a prime number, \( n(E) \) is the number of favorable outcomes (39), and \( n(S) \) is the total number of possible outcomes (260).

4. **Substitute the Values into the Formula**:
\[ P(E) = \frac{39}{260} \]

5. **Simplify the Fraction**:
- To simplify \( \frac{39}{260} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 13:
\[ P(E) = \frac{39 \div 13}{260 \div 13} = \frac{3}{20} \]

6. **Conclusion**:
- Therefore, the probability of getting a prime number when a die is thrown is \( \frac{3}{20} \).

### Final Answer:
The probability of getting a prime number is \( \frac{3}{20} \).