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Ten fair coins: the average and a particular outcome
mathematics
Flip a fair coin ten times. On average five come up heads; the chance of exactly two heads is C(10,2)/2¹⁰. The engine confirms both the expectation and the exact probability. Worked & sealed by the engine — E[Binom(10, ½)] = n·p = 5 · P(X=2) = C(10,2)·½¹⁰ = 45/1024 ≈ 0.04395. [HOLDS; open the seal to re-check.]
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card_works_probability
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adjoining cards
- on the shelf of → The Works — sealed, worked demonstrations — a member of the the-works shelf in the keeping
- 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 → 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).
- demonstrates → P(ill | +) = (.9·.01)/(.9·.01 + .05·.99) ≈ 0.154 — A worked demonstration in the same field (probability).
- kindred → The base rate a doctor must not forget — A sibling worked demonstration in probability.
- adjacent → Vectors and matrices: a dot product and a determinant — Neighbouring worked demonstrations in the same part of the volume.
- adjacent → Measuring information: one bit, and a distance — Neighbouring worked demonstrations in the same part of the volume.
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