To find the probability that a randomly chosen number between 1 and 300 is divisible by 4, follow these steps:

1. Determine the total number of possible outcomes:
- The total number of integers between 1 and 300 is 300.

2. Determine the number of favorable outcomes:
- A number is divisible by 4 if it can be written in the form \( 4k \), where \( k \) is an integer.
- The smallest number divisible by 4 in this range is 4, and the largest is 300.
- To find how many such numbers there are, use the formula for the \( n \)-th term of an arithmetic sequence:
\[
a_n = 4 + (n-1) \times 4
\]
Set \( a_n \) to 300 to find \( n \):
\[
300 = 4 + (n-1) \times 4
\]
\[
300 = 4 + 4n - 4
\]
\[
300 = 4n
\]
\[
n = \frac{300}{4} = 75
\]
- So, there are 75 numbers between 1 and 300 that are divisible by 4.

3. Calculate the probability:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\]
\[
\text{Probability} = \frac{75}{300} = \frac{1}{4}
\]


The probability that the number chosen is divisible by 4 is \(\frac{1}{4}\).

The correct answer is B. \(\frac{1}{4}\).