To solve this problem, we need to find the probability of getting a number between 1 and 100 that is divisible by one and itself only. This is equivalent to finding the probability of selecting a prime number from the given range.

Let's break down the problem into smaller steps:

Step 1: Find the total number of favorable outcomes.
To find the total number of prime numbers between 1 and 100, we can list them: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. There are a total of 25 prime numbers in the given range.

Step 2: Find the total number of possible outcomes.
The total number of possible outcomes is the number of integers between 1 and 100, inclusive. This can be calculated as (100 - 1) + 1 = 100.

Step 3: Calculate the probability.
The probability is given by the formula:
Probability = Number of favorable outcomes / Number of possible outcomes

So, the probability of getting a prime number between 1 and 100 is:
Probability = 25 / 100

Simplifying the fraction, we get:
Probability = 1 / 4

Therefore, the correct answer is option 'C': 1/4 or 25/100.

Explanation:
The probability of getting a number between 1 and 100 that is divisible by one and itself only is equivalent to the probability of selecting a prime number. By listing all the prime numbers between 1 and 100, we find that there are 25 such numbers. The total number of possible outcomes is 100, as there are 100 integers between 1 and 100. Dividing the number of favorable outcomes (25) by the number of possible outcomes (100) gives us a probability of 1/4 or 25/100. Therefore, the correct answer is option 'C'.