What is the probability that a number selected from the numbers 1,2,3,…25 is a prime number ? You may assume that each of the 25 numbers is equally likely to be selected .

Answer

To find the probability that a number selected from the numbers 1 to 25 is a prime number, we can follow these steps:

### Step 1: Identify the total number of outcomes
The total outcomes are the numbers from 1 to 25. Thus, the total number of outcomes is:
\[ \text{Total outcomes} = 25 \]

### Step 2: Identify the prime numbers between 1 and 25
Prime numbers are numbers greater than 1 that have no positive divisors other than 1 and themselves. The prime numbers between 1 and 25 are:
- 2
- 3
- 5
- 7
- 11
- 13
- 17
- 19
- 23

### Step 3: Count the number of prime numbers
Now, we count the prime numbers identified in Step 2. The prime numbers are:
- 2, 3, 5, 7, 11, 13, 17, 19, 23

Thus, the total number of prime numbers is:
\[ \text{Number of prime numbers} = 9 \]

### Step 4: Calculate the probability
The probability \( P \) of selecting a prime number is given by the formula:
\[ P(\text{prime}) = \frac{\text{Number of prime numbers}}{\text{Total outcomes}} = \frac{9}{25} \]

### Final Answer
Therefore, the probability that a number selected from the numbers 1 to 25 is a prime number is:
\[ \frac{9}{25} \]

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