{"query": "Ten fair coins: the average and a particular outcome", "count": 20, "results": [{"id": "card_works_probability", "title": "Ten fair coins: the average and a particular outcome", "shelf": "the-works", "surface": "secular", "snippet": "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 e", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_theory_measure_theory__lebesgue_integration", "title": "Measure theory (Lebesgue integration)", "shelf": "theories", "surface": "secular", "snippet": "Measure theory (Lebesgue integration) — an engine domain that can touch it: mathematics. Calibration: map-only — a foundation, not a computation. What it means for a set to have a SIZE, done carefully", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_alm_connection_entropy_is_thermodynamic", "title": "Almanac: Shannon entropy and thermodynamic entropy are the same quantity", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  The entropy of a message and the entropy of a gas are not analogies -- they are one formula. information_theory confirmed Shannon entropy numerically: a fair coin carries 1 bit, four equal", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_works_information", "title": "Measuring information: one bit, and a distance", "shelf": "the-works", "surface": "secular", "snippet": "A single fair coin carries exactly one bit of Shannon entropy; the Hamming distance counts how many positions two codewords differ in — the ground of error correction.  Worked & sealed by the engine —", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_n_3527e5d13060", "title": "Luke 15", "shelf": "codex", "surface": "witness", "snippet": "1. Now all the tax collectors and sinners were coming close to him to hear him.\n2. The Pharisees and the scribes murmured, saying, “This man welcomes sinners, and eats with them.”\n3. He told them this", "authority_tier": "scripture", "source": "World English Bible · Luke 15", "readable": false, "generated": false}, {"id": "card_alm_connection_independence_multiplies_information_adds", "title": "Almanac: Independence multiplies probability but adds information", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  Flip two fair coins. The probability verifier confirmed that independent events MULTIPLY: P(A and B) = 0.5 x 0.5 = 0.25. The information_theory verifier confirmed that one fair coin carrie", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_n_8c0a8e10c3da", "title": "Ignatius to the Magnesians V", "shelf": "patristics", "surface": "witness", "snippet": "Seeing, then, all things have an end, these two things are simultaneously set before us—death and life; and every one shall go unto his own place. For as there are two kinds of coins, the one of God, ", "authority_tier": "father", "source": "Ignatius to the Magnesians (shorter recension; trans. Roberts-Donaldson, 1885)", "readable": false, "generated": false}, {"id": "card_src_openstax_introductory_statistics_2e_3_1_terminology_1a2f7d70", "title": "3.1 Terminology — Introductory Statistics 2e", "shelf": "mathematics", "surface": "secular", "snippet": "3.1\n\nTerminology\n\nProbability is a measure that is associated with how certain we are of outcomes of a particular experiment or activity. An experiment is a planned operation carried out under control", "authority_tier": "reference", "source": "OpenStax: Introductory Statistics 2e (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_introductory_statistics_3_1_terminology_1a2f7d70", "title": "3.1 Terminology — Introductory Statistics", "shelf": "mathematics", "surface": "secular", "snippet": "3.1\n\nTerminology\n\nProbability is a measure that is associated with how certain we are of outcomes of a particular experiment or activity. An experiment is a planned operation carried out under control", "authority_tier": "reference", "source": "OpenStax: Introductory Statistics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_introductory_business_statistics_2e_3_1_terminology_a72fed3e", "title": "3.1 Terminology — Introductory Business Statistics 2e", "shelf": "mathematics", "surface": "secular", "snippet": "3.1\n\nTerminology\n\nProbability is a measure that is associated with how certain we are of outcomes of a particular experiment or activity. An experiment is a planned operation carried out under control", "authority_tier": "reference", "source": "OpenStax: Introductory Business Statistics 2e (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_introductory_business_statistics_3_1_terminology_a72fed3e", "title": "3.1 Terminology — Introductory Business Statistics", "shelf": "mathematics", "surface": "secular", "snippet": "3.1\n\nTerminology\n\nProbability is a measure that is associated with how certain we are of outcomes of a particular experiment or activity. An experiment is a planned operation carried out under control", "authority_tier": "reference", "source": "OpenStax: Introductory Business Statistics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_word_coin_collection", "title": "coin collection", "shelf": "dictionary", "surface": "secular", "snippet": "coin collection: (noun) a collection of coins · (noun) the collection and study of money (and coins in particular) — syn: numismatics, numismatology, coin collecting", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_word_coin_collecting", "title": "coin collecting", "shelf": "dictionary", "surface": "secular", "snippet": "coin collecting: (noun) the collection and study of money (and coins in particular) — syn: numismatics, numismatology, coin collection", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_openstax_introductory_statistics_4_2_mean_or_expected_value_and_standard__2779d41f", "title": "4.2 Mean or Expected Value and Standard Deviation — Introductory Statistics", "shelf": "mathematics", "surface": "secular", "snippet": "4.2\n\nMean or Expected Value and Standard Deviation\n\nThe expected value is often referred to as the \"long-term\" average or mean. This means that over the long term of doing an experiment over and over,", "authority_tier": "reference", "source": "OpenStax: Introductory Statistics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_introductory_statistics_2e_4_2_mean_or_expected_value_and_standard__2779d41f", "title": "4.2 Mean or Expected Value and Standard Deviation — Introductory Statistics 2e", "shelf": "mathematics", "surface": "secular", "snippet": "4.2\n\nMean or Expected Value and Standard Deviation\n\nThe expected value is often referred to as the \"long-term\" average or mean. This means that over the long term of doing an experiment over and over,", "authority_tier": "reference", "source": "OpenStax: Introductory Statistics 2e (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_book_51302", "title": "English Coins and Tokens, with a Chapter on Greek and Roman Coins — Llewellynn Frederick William Jewitt", "shelf": "gutenberg", "surface": "secular", "snippet": "English Coins and Tokens, with a Chapter on Greek and Roman Coins, by Llewellynn Frederick William Jewitt. Subjects: Tokens -- Great Britain; Numismatics -- Great Britain; Coins, British. Read the ful", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "readable": true, "generated": false}, {"id": "card_src_etym_denier", "title": "denier", "shelf": "etymology", "surface": "secular", "snippet": "denier: etymology (Webster 1913) — n.: [F. denier, fr. L. denarius a Roman silver coin orig. equiv. to ten asses, later, a copper, fr. deni ten by ten, fr. the root of decem ten; akin to E. ten. See T", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_src_book_26866", "title": "Le monete dei possedimenti veneziani di oltremare e di terraferma descritte ed illustrate da Vincenzo Lazari — Vincenzo Lazari", "shelf": "gutenberg", "surface": "secular", "snippet": "Le monete dei possedimenti veneziani di oltremare e di terraferma descritte ed illustrate da Vincenzo Lazari, by Vincenzo Lazari (in it). Subjects: Numismatics -- Italy -- Venice (Province) -- History", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "readable": true, "generated": false}, {"id": "card_src_openstax_statistics_3_1_terminology_02cc8ca2", "title": "3.1 Terminology — Statistics", "shelf": "mathematics", "surface": "secular", "snippet": "3.1\n\nTerminology\n\nProbability is a measure that is associated with how certain we are of results, or outcomes, of a particular activity. When the activity is a planned operation carried out under cont", "authority_tier": "reference", "source": "OpenStax: Statistics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_lex_g2772", "title": "G2772 — κέρμα (kerma): coin", "shelf": "lexicon", "surface": "secular", "snippet": "κέρμα (kerma), Strong's G2772: coin. κέρμα , -τος, τό (κείρω), __1. a slice, hence, __2. a small coin : pl., Jhn.2:15. † (AS)", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_works_probability"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}