LEARN · EXPLAIN · REVISE

A program’s pseudo-random outputs are reused with the same seed. Does that create new independent evidence each rerun?

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

高一必修第二册(A版).pdf · 10.3 · PDF 261 / printed page 254

TOPIC 01

Frequency and probability

Build understanding of frequency and probability through definitions, contrasting cases and justified applications.

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

01 / Standard#Your turn

n=30

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Distinguish observed relative frequency from a model probability and describe the experiment.

Hint 2

Inspect whether the sequence actually changes.

Worked solution

Distinguish observed relative frequency from a model probability and describe the experiment.
Calculate or simplify this relation.
$\text{same seed}\Rightarrow\text{same deterministic sequence}$
Reproducibility is valuable but does not multiply the number of independent runs.

No; reproducing the same sequence repeats the same simulated observations.

Checks and common pitfalls: Reproducibility is valuable but does not multiply the number of independent runs.

Reasoning checklist · self / teacher assessment

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

Teacher preparation and assessment

Use frequency and probability to state a justified conclusion.
Relative frequency: The observed fraction estimates a model probability over repeated trials.
Finite-sample uncertainty: A long-run tendency does not force exact agreement in every finite sample.
Close with: conditions → representation → reasoning → check.

Expected reasoning: The observed fraction estimates a model probability over repeated trials.
Expected reasoning: A long-run tendency does not force exact agreement in every finite sample.
Expected correction: Previous independent outcomes do not create compensation on the next trial.