What you’ll learn
Understand random sampling.
Key idea
Uniform selection of a fixed-size distinct sample gives equal inclusion chance, not certainty about a sample's composition.
Random requires a chance mechanism over the full frame; it does not guarantee exactly matching every subgroup in one sample.
Worked example
Enter the exact value or ordered values in the format requested below.
A simple random sample chooses 3 distinct IDs uniformly without replacement from all 60 school pupils. Enter the exact probability that one specified pupil is included.
- The full roster has 60 unique pupil IDs, all treated symmetrically by a uniform shuffle.
- Taking 3 distinct positions gives each specified pupil inclusion probability 3/60=1/20; it does not guarantee any particular sample composition.
Answer: 1/20
Quick Check
Interpret the result of 'Understand random sampling' in the data-generating context, including units and population limits.
A school roster has 90 unique pupil IDs; a uniform shuffle selects the first 14 without replacement. Interpret this sampling procedure and its limitation.