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Data, probability and statistics I · Lesson 09 / 12

Simulate and allow for variation

A 75% chance does not promise exactly 75 blue tokens in every set of 100 draws. Simulation helps reveal the difference between model and outcome.

Learning paths18 min

Let's discover together

  1. 1

    Set three blue tokens, 100 draws and seed 42. Before running, predict a plausible range of outcomes. Record observed blues/100 and compare with 3/4. The workshop generates model outcomes; it does not observe a real bag.

  2. 2

    Repeat with the same seed: the algorithm generates the same sequence. This helps someone check your report but supplies no new independent observations. Record seed, composition, count and replacement.

  3. 3

    Compare seeds 1, 42 and 123 using 10, 100 and 1000 draws. Across independent model repetitions, frequencies tend to stabilize with more trials; a particular longer run can still be farther from 75% than a shorter one.

  4. 4

    More draws do not fix a wrong model. For delivery samples, more cases also do not automatically remove selection bias. Separate random variation, data quality and validity of the rules.

Evidence lab

Experiment with fictional deliveries at Aurora station. Analysis runs in this browser. Nothing entered here is sent to the server.

The workshop resets when you leave or reload. Download data and report to keep your work, or send the report to the activity editor, which keeps a draft in this browser. Completion and XP belong to the account.

Header id,group,minutes; one delivery per row; unique id; groups A/B; decimal point; duration 0–1440 with up to two decimal places. Blank means unknown. Up to 100 rows. No quotes or decimal commas. Use invented data.

Selection uses the entered table, including missing values. A draw does not guarantee representativeness. The same seed reproduces selection; it cannot recover cases outside the table.

Make a prediction and analyze the table.

Virtual bag: model with replacement

There are four equally likely tokens; choose how many are blue. Each token returns before the next draw. This is a deterministic simulation, without prizes, money or real observations.

Repeating the seed repeats the sequence. More draws do not guarantee a closer result in every run and do not validate the real-world model.

Two rules, the same accuracy

Ten fictional cases: nine normal and one failure. Rules defined for this example; no AI training or real equipment testing. Same number correct, different consequences.

Two rules, the same accuracy
RuleCorrect / totalMissed failuresFalse alarms

Your investigation report

Official links and next step

✦
YOUR MISSION

Compare theoretical probability with observed frequency without treating simulation as proof.

Now it's your turn

Discovery workshop

Predict, check, explain

Compare theoretical probability with observed frequency without treating simulation as proof.
Build your answers and check when you are ready.
A moment to understand

What does repeating the exact same seed and settings mean?

I need a hint

Reproduction allows checking; it does not eliminate uncertainty or validate the model. Observed frequency and theoretical probability are different objects.

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Take it with you

Make a table of three seeds and two draw counts. Record your prediction before running and a conclusion that avoids “always”. Then repeat one row to check reproducibility.

At your own pace

My files and GitHub

Every lesson can become your own record: code, notes or a practice plan. Saving a file to GitHub is optional and does not change your XP.

Student guide

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