Out of one digit prime numbers, one number is selected at random. The probability of selecting an even number is:

Options

A. `(1)/(2)`
B. `(1)/(4)`
C. `(4)/(9)`
D. `(2)/(3)`

Answer

To solve the problem of finding the probability of selecting an even one-digit prime number, we can follow these steps:

### Step 1: Identify one-digit prime numbers
The one-digit prime numbers are:
- 2
- 3
- 5
- 7

So, the complete list of one-digit prime numbers is: **2, 3, 5, 7**.

### Step 2: Count the total number of one-digit prime numbers
From the list, we can see that there are a total of **4 one-digit prime numbers**.

### Step 3: Identify the even one-digit prime numbers
Among the one-digit prime numbers, we need to identify the even ones. The only even prime number is:
- **2**

So, there is only **1 even one-digit prime number**.

### Step 4: Calculate the probability
The probability \( P \) of selecting an even number can be calculated using the formula:

\[ P(\text{even prime}) = \frac{\text{Number of favorable outcomes (even primes)}}{\text{Total number of outcomes (one-digit primes)}} \]

Substituting the values we found:
- Number of favorable outcomes (even prime numbers) = 1
- Total number of outcomes (one-digit prime numbers) = 4

Thus, the probability is:

\[ P(\text{even prime}) = \frac{1}{4} \]

### Final Answer
The probability of selecting an even one-digit prime number is **\(\frac{1}{4}\)**.

---