Module 3: Probability & Statistics: Mistake Clinic

This clinic turns wrong moves into reusable judgment. Use it after each practice page and again before the quiz or checkpoint.

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Module-Specific Mistake Radar

Start with these traps. Replace or extend them with real mistakes from your own work.

Mistake to look for	Where it shows up	Symptom	Repair evidence
Finishing Probability Modeling and Conditioning Lab with only a final answer	Probability Modeling and Conditioning Lab	The work has no failed case, trace, test, proof gap, or design stress point.	Add the smallest broken example and show the repair that changes the result.
Finishing Random Variables and Distribution Workshop with only a final answer	Random Variables and Distribution Workshop	The work has no failed case, trace, test, proof gap, or design stress point.	Add the smallest broken example and show the repair that changes the result.
Finishing Expectation, Variance, and Statistical Reasoning Clinic with only a final answer	Expectation, Variance, and Statistical Reasoning Clinic	The work has no failed case, trace, test, proof gap, or design stress point.	Add the smallest broken example and show the repair that changes the result.
Finishing Code Katas with only a final answer	Code Katas	The work has no failed case, trace, test, proof gap, or design stress point.	Add the smallest broken example and show the repair that changes the result.
Treating Probability Starts with a Well-Defined Model as vocabulary instead of a tool	Probability Starts with a Well-Defined Model	The explanation names the concept but cannot decide between two cases.	Write one example, one non-example, and the rule that separates them.
Treating Counting Models, Equally Likely Outcomes, and Event Algebra as vocabulary instead of a tool	Counting Models, Equally Likely Outcomes, and Event Algebra	The explanation names the concept but cannot decide between two cases.	Write one example, one non-example, and the rule that separates them.

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Practice Mistake Checks

Pull any miss from these checks into your mistake log.

Probability Modeling and Conditioning Lab

Source: practice/01-probability-modeling-and-conditioning-lab.md

For each statement, identify the error:

1. "There are three possible sums when two coins are flipped: 0, 1, 2, so each has probability 1/3."
2. "The test is 99% accurate, so a positive result means a 99% chance the disease is present."
3. "Events that cannot happen together are independent."
4. "At least one failure means add the failure probabilities directly."

Random Variables and Distribution Workshop

Source: practice/02-random-variables-and-distribution-workshop.md

For each statement, identify the error:

1. "A random variable is just the event written with a capital letter."
2. "Sampling without replacement from a finite deck is binomial because there are only two outcomes."
3. "P(X <= 3) is the same thing as P(X = 3) if the support is discrete."
4. "The Poisson model is correct whenever the answer is a count."

Expectation, Variance, and Statistical Reasoning Clinic

Source: practice/03-expectation-variance-and-statistical-reasoning-clinic.md

For each statement, identify the error:

1. "Linearity of expectation requires independence."
2. "Since the expected value is 3.5, the next roll is likely to be 3.5 in effect."
3. "Zero covariance always implies independence."
4. "A 95% confidence interval means a 95% probability the fixed parameter is inside it."
5. "The LLN means a tail is due after many heads."

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Repair Protocol

For each real mistake:

1. Reproduce the failure on the smallest example, trace, proof, query, command, or design sketch.
2. Name the hidden assumption.
3. Repair the artifact.
4. Save evidence that changed: failing then passing test, corrected proof step, revised diagram, safer command, benchmark, or review note.
5. Add one retrieval card beginning with Check... before... or Do not use... when....

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Mistake Log

Date	Mistake	Symptom	Root cause	Repair evidence	Retrieval card
Starter	Pick one radar row above	Explain how it would fail in this module	Name the assumption	Add a counterexample or corrected artifact	Write the card before closing the page

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Completion Standard

• At least five real mistakes are logged.
• At least two mistakes include a counterexample or failing test.
• At least one mistake connects to an older semester skill.
• At least one correction changes code, a proof, a diagram, a command transcript, a query, or a design decision.