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Walk me through Bayes' theorem on a real diagnostic problem: why can a 99%-accurate test still be wrong most of the time it fires?

The base-rate trap is the classic, and it is not academic: it is exactly how a high-accuracy fraud or disease classifier drowns ops in false alarms. The worked numbers, the tree you draw on the whiteboard, and the two levers that actually fix it in production.

Updated Sep 2026 · Grounded in real Forward Deployed Engineer interview loops and written to a senior-engineer editorial bar.

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FEDITOR'S NOTE

The screen is whether the candidate computes the posterior correctly and, more importantly, connects it to a deployment failure (alert fatigue, swamped review queues) and to the fixes (raise the threshold, add a second independent test, or restrict to a higher-base-rate sub-population). The reserved follow-up is 'your fraud model is 99% accurate and ops says it's useless, why': the answer is the base rate, and a candidate who reaches for that unprompted is the strong one.

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