Probability
The mathematics of chance: a way to put a number on how likely an uncertain event is, and to compute the fair value of a bet by weighing each possible outcome by its probability. Uncertainty, long thought the province of fate, becomes something you can calculate.
الأرشيف العميق مكتوب بالإنجليزية حتى الآن — والترجمات المتحقَّق منها جزء من خارطة الطريق. خاصية الترجمة في متصفحك تعمل جيدًا في هذه الصفحة.
✦ مهلًا، حقًّا؟
The entire field was born from a gambler's grievance. Around 1654 the Chevalier de Méré, a French nobleman and dice player, asked Blaise Pascal how to fairly split the pot if a game is stopped before anyone wins. Pascal wrote to Pierre de Fermat, and the handful of letters they exchanged that summer — solving the "problem of points" two different ways and agreeing on the answer — founded the mathematics now underneath all insurance, statistics, and risk.
ما هو
Probability theory attaches a number between 0 and 1 to an uncertain event — 0 for impossible, 1 for certain — and gives rules for combining those numbers. Its central invention is *expected value*: the worth of an uncertain prospect is each possible payoff multiplied by its probability, all added up. That single quantity tells you what a bet is really worth, what a wager should cost, what you should expect to win or lose per play over the long run. Blaise Pascal and Pierre de Fermat worked it out in a 1654 exchange of letters.
لماذا كان مهمًّا
Chance had always seemed the opposite of mathematics — the domain of luck, fate, and the gods, the thing you *couldn't* reason about. Pascal and Fermat showed it obeys exact laws. The immediate problem was trivial-sounding: two players are interrupted mid-game, one leading; how should the stakes be divided? The wrong-but-obvious answers (split evenly, or in proportion to current score) are both unfair. The right answer weights the division by each player's *chance of eventually winning* from the current position — which requires enumerating the possible futures. Getting that right meant inventing a way to reason about events that have not happened yet.
ما الذي أتاحه
Within decades the theory was formalized by Huygens and then Jacob Bernoulli, whose law of large numbers explained why long-run frequencies converge on their probabilities. From there it became the mathematics of the actuarial tables that made life insurance possible, of statistics and the census, of statistical mechanics in physics, of quantum theory, of quality control, and of information theory — Shannon's measure of information is built directly on probability. The letters two Frenchmen swapped about a dice game turned out to be the foundation for how the modern world prices and manages uncertainty.
أدنى نسخة صالحة للعمل
List every equally likely outcome of a game of chance; the probability of an event is the fraction of outcomes in which it happens, and the fair value of a stake is each prize multiplied by its probability, summed — the expected value.
هذا المدخل في انتظار سرده الكامل — رسّامو الخرائط يعملون عليه. أما موضعه في الشبكة فمُتحقَّق منه بالفعل.
يقتضي
خيوط تمرّ بهذه القدرة
How did a coffee house become the insurance industry?6 خطوةالمصادر
- — The Pascal–Fermat correspondence (summer 1654)
- — Ian Hacking, *The Emergence of Probability* (1975)
- — Keith Devlin, *The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern* (2008)
هل في هذه الصفحة خطأ؟ كل زعم هنا كُتب ليصمد أمام التحدي. اقترح تصحيحًا →