Arun

Simple Random Sampling (SRS)

In Simple Random Sampling, every individual in the population has an equal and independent probability of being selected.

Mathematical Description

Let:

• \(N\) = population size
• \(n\) = sample size

Then the probability that any specific unit is selected is:
$$ P(\text{selection}) = \frac{n}{N} $$
Each possible sample of size \(n\) has equal probability:
$$ P(\text{any given sample}) = \frac{1}{\binom{N}{n}} $$

Example:

If a class has 100 students and you randomly select 10 students, each student has a probability of 0.1 of being chosen.

When to Use:

• Population is homogeneous
• Complete sampling frame is available
• Simple and unbiased selection