About the Sample Selection Probability
This calculator finds the probability that any one specific individual ends up chosen in a simple random sample, given the size of the population and the size of the sample being drawn. It is a quick way to check how representative or how thin a planned sample will feel for the people or items being sampled from.
How It Works
Enter the total population size and the planned sample size. The calculator divides the sample size by the population size and expresses the result as a percentage, reflecting the defining property of a simple random sample: every member of the population has an identical chance of being selected.
Examples
Customer Survey Pool
Drawing a sample of 200 from a population of 5,000 gives a selection probability of (200 / 5,000) × 100 = 4.000%.
Large-Scale Audit
Drawing a sample of 1,000 from a population of 50,000 gives a selection probability of (1,000 / 50,000) × 100 = 2.000%, half the rate of the smaller pool despite a larger sample.
Advantages
- Gives a precise, unambiguous number for how likely any single individual is to be included, useful for explaining sampling fairness to stakeholders.
- Highlights the inverse relationship between population size and individual selection odds, which helps when planning how large a sample needs to be.
- Simple two-input design means the check takes seconds rather than requiring a full sampling frame to be built first.
Common Mistakes
- Applying the equal-probability result to sampling methods other than true simple random sampling, such as stratified or quota sampling, where selection odds intentionally differ by subgroup.
- Confusing an individual's selection probability with the sample's share of the total population used for other purposes, like weighting survey results.
- Assuming a higher sample size alone guarantees a representative sample, when the sampling method and coverage of the population matter just as much as the count.
Edge Cases to Watch For
- Population size must be greater than zero, or the calculator returns an error.
- Sample size cannot exceed population size; the calculator rejects that input rather than returning a probability over 100%.
- The formula assumes every individual truly has an equal, independent chance of selection, which only holds for a genuine simple random sample, not for stratified, cluster, or convenience sampling designs.
Common Use Cases
- Researchers designing a survey who want to state each participant's chance of being contacted.
- Auditors selecting a random subset of transactions or records for review and needing to document the selection odds.
- Students and analysts learning the mechanics of simple random sampling before moving to more complex designs.