LEARN · EXPLAIN · REVISE

A population has 100k students and a simple random sample has 10k. Find each student’s inclusion probability.

Read the idea, work independently, then explain what changed.

高一必修第二册(A版).pdf · 9.1 · PDF 180 / printed page 173

TOPIC 01

Random sampling

Build understanding of random sampling through definitions, contrasting cases and justified applications.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Worked example

k=2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Identify the population and sampling mechanism before scaling counts.

Hint 2

All students must have the same chance under simple random sampling.

Worked solution

The requested value is 0.1.

Checks and common pitfalls: This is inclusion probability, not the fraction who will answer a survey.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment

Use random sampling to state a justified conclusion.
Sampling design: Simple random, systematic and stratified procedures define how units are selected.
Error sources: Coverage, nonresponse and measurement problems differ from random sampling variation.
Close with: conditions → representation → reasoning → check.

Expected reasoning: Simple random, systematic and stratified procedures define how units are selected.
Expected reasoning: Coverage, nonresponse and measurement problems differ from random sampling variation.
Expected correction: A larger sample does not automatically remove selection bias.