Probability a negative review came from a lazy reviewer

Q: Probability a negative review came from a lazy reviewer

Evaluates Bayes' theorem for reviewer-type inference from a negative review under strict reviewer behavior assumptions. Strong answers define lazy and careful reviewer priors, compute the marginal negative-review probability, and explain why the posterior for lazy is zero.

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Question

Bayesian Posterior: Negative Review and Lazy Reviewer

Reviewer types in the population:

Lazy reviewers are 20% of reviewers and never leave negative feedback.
Careful reviewers are 80% of reviewers and leave positive feedback 60% of the time and negative feedback 40% of the time.

Given that you observe a negative review, what is the probability it was written by a lazy reviewer?

Constraints & Assumptions

Use Bayes' theorem.
Treat "never leave negative feedback" as probability zero.
Define reviewer types and the observed negative-review event.
Explain the intuition behind the posterior.

Clarifying Questions to Ask Guidance

Is "never" literal, or should it be treated as a very small probability?
Are lazy and careful reviewers the only reviewer types?
Is the observed review randomly sampled from all reviews?
Are review probabilities independent across reviews?

What a Strong Answer Covers Guidance

Defines L for lazy, C for careful, and N for negative review.
Uses P(L) = 0.2, P(C) = 0.8, P(N | L) = 0, and P(N | C) = 0.4.
Computes P(N) = 0 times 0.2 plus 0.4 times 0.8 = 0.32.
Computes P(L | N) = 0.
Explains that under the stated assumptions a negative review cannot come from a lazy reviewer.
Notes how the answer would change if lazy reviewers had a small nonzero negative-review rate.

Follow-up Questions Guidance

What if lazy reviewers leave negative reviews 1% of the time?
What is P(Careful | Negative)?
How would you estimate these probabilities from data?

Probability a negative review came from a lazy reviewer

Quick Overview

Probability a negative review came from a lazy reviewer

Bayesian Posterior: Negative Review and Lazy Reviewer

Constraints & Assumptions

Clarifying Questions to Ask Guidance

What a Strong Answer Covers Guidance

Follow-up Questions Guidance

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