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The base rate a doctor must not forget
mathematics
A disease affects 1 in 100. A test is 90% sensitive and has a 5% false-positive rate. A positive result feels alarming — yet Bayes' theorem shows the chance of actually being ill is only about 15%. The base rate rules. Worked & sealed by the engine — P(ill | +) = (.9·.01)/(.9·.01 + .05·.99) ≈ 0.154. [HOLDS; open the seal to re-check.]
source
card id
card_works_bayes
address
UNPLACED
adjoining cards
- on the shelf of → The Works — sealed, worked demonstrations — a member of the the-works shelf in the keeping
- kindred → Ten fair coins: the average and a particular outcome — A sibling worked demonstration in probability.
- paves → The Floor of Discovery — one floor, and by its design the fear of God — A worked, engine-sealed demonstration — a paving-stone of the floor of reality.
- demonstrates → P(ill | +) = (.9·.01)/(.9·.01 + .05·.99) ≈ 0.154 — A worked demonstration in the same field (probability).
- demonstrates → E[Binom(10, ½)] = n·p = 5 · P(X=2) = C(10,2)·½¹⁰ = 45/1024 ≈ 0.04395 — A worked demonstration in the same field (probability).
- adjacent → The integers, examined: a prime, a divisor, a factorial — Neighbouring worked demonstrations in the same part of the volume.
- adjacent → A p-value against a threshold — Neighbouring worked demonstrations in the same part of the volume.
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