Business Context

Meta is evaluating a lightweight classifier that flags potentially bad Instagram Reels before ranking. The model is being considered as an upstream filter in the AARRR funnel because false alarms can suppress healthy creator distribution, while misses can hurt integrity.

Problem Statement

A classifier used on Instagram Reels has 95% true positive rate and 95% true negative rate for detecting bad content. The underlying prevalence of actually bad Reels is only 1%. You need to determine the probability that a Reel is actually bad given that the classifier predicted bad.

Given Data

Here, $B$ means actually bad, $G$ means actually good, and $\hat{B}$ means predicted bad.

Requirements

1. Compute the false positive rate from the true negative rate.
2. Use Bayes' theorem to calculate $P(B \mid \hat{B})$.
3. Verify the answer with a confusion-matrix style count using 1,000,000 Reels.
4. Briefly explain why this result matters for product decisions on Instagram Reels ranking and integrity.

Assumptions

• The classifier is evaluated on traffic representative of production Reels inventory.
• The 1% prevalence is stable during the measurement window.
• Each Reel is treated independently.
• Ignore downstream effects such as novelty effect, SRM, or CUPED adjustment; this is a pure conditional probability question.