概率

出自維基百科,自由嘅百科全書
(由或然率跳轉過嚟)
跳去導覽 跳去搵嘢
輪盤(上)、掟銀仔(左下)同擲骰仔(右下)一般俾人認為係本質上隨機性嘅事件

概率粵拼koi3 leot2英文probability),又叫機會率機率或然率,係指一件事件有幾可能係真(或者一個結果出現嘅可能程度):概率可以用百分比寫出嚟-介乎 0 同 1 之間,100% 代表件事實會發生,0% 代表件事絕對唔會發生,50% 就表示件事「有 50% 機會發生」;例如家陣掟一個銀仔,假設個銀仔冇出千嘅話,應該會有 50% 機會出公、50% 機會出字,而呢件事嘅結果(公定字)原則上係冇可能預測嘅,反映咗不確定性(uncertainty)[1][2]

基礎[編輯]

睇埋:概率論

概率可以噉樣想像:家陣有若干件可能嘅事件,而分析者同每一個可能嘅事件都俾一個數值佢;每件事件掕住嗰個數值就係嗰件事件嘅概率 ,用日常用語講表示「件事件有幾大機會發生」,0 表示「實唔會發生」,1 表示「實會發生」。响廿一世紀嘅概率論(probability theory)當中,啲人一般會用以下噉嘅數學符號嚟表示所講嘅嘢[3]

  • 啲人一般會用「」或者「」嚟代表「 發生嘅概率」,
  • 而一場實驗嘅結果()可以用噉嘅方式表達[4]
    嘅概率係 」、「 嘅概率係 」... 呀噉; 可以想像成(例如)「擲骰仔得到嘅數」。
Fair dice probability distribution.svg

概率可以用好似上圖噉嘅方式嚟表達;想像 X 軸,表示「擲一粒六面骰仔得到嘅數」,而 Y 軸表示各件呢啲事件嘅相應 值。假如粒骰仔冇出千,應該每個數出現嘅概率都係一樣嘅。

詮釋[編輯]

內文:概率嘅詮釋

喺概率論史上,「概率呢個數值要點樣理解」係一個有相當爭議性嘅問題:喺最基本上,古典嘅決定論(determinism)主張,如果一個觀察者喺而家呢一刻完美知道嗮宇宙嘅狀態(例:知道每粒原子喺乜位置同以乜嘢速度郁緊等等),佢將會有能力靠物理定律-假設佢識嗮所需嘅物理知識-完美預測宇宙下一刻嘅狀態(可以睇吓拉普拉斯魔[5],所以概率呢個數值淨係反映人類知識唔夠,而主張呢個觀點嘅人會話「人之所以預測唔到掟銀仔嘅結果,係因為人知唔嗮風向等嘅資訊[6][7]。不過廿世紀量子力學(quantum mechanics)研究指出,宇宙裏面有部份嘅事件似乎係本質上就冇可能完全準確噉預測嘅,人頂櫳都淨係有得估呢啲事件發生嘅概率[8]

研究史[編輯]

16世紀,卡丹奴喺佢嘅著作 Liber de Ludo Aleae 中最早推算或然率,而最早有系統研究或然率嘅,就係法國數學家費馬帕斯卡

睇埋[編輯]

[編輯]

  1. William Feller, An Introduction to Probability Theory and Its Applications, (Vol 1), 3rd Ed, (1968), Wiley.
  2. Kallenberg, O. (2006). Foundations of modern probability. Springer Science & Business Media.
  3. Bain, Lee J.; Engelhardt, Max (1992). Introduction to Probability and Mathematical Statistics (2nd ed.). Belmont, California: Brooks/Cole. p. 53.
  4. Murphy, K. P. (2012). Machine learning: a probabilistic perspective, p. 35. MIT press.
  5. Richard Langdon Franklin (1968). Freewill and determinism: a study of rival conceptions of man. Routledge & K. Paul.
  6. Laplace, Pierre Simon. A Philosophical Essay on Probabilities, translated into English from the original French 6th ed. by Truscott, F.W. and Emory, F.L., Dover Publications (New York, 1951).
  7. Moore, W.J. (1992). Schrödinger: Life and Thought. Cambridge University Press. p. 479.
  8. Stephen Hawking's Grand Design (2010), page 32: "the molecular basis of biology shows that biological processes are governed by the laws of physics and chemistry and therefore are as determined as the orbits of the planets...so it seems that we are no more than biological machines and that free will is just an illusion", and page 72: "Quantum physics might seem to undermine the idea that nature is governed by laws, but that is not the case. Instead it leads us to accept a new form of determinism: Given the state of a system at some time, the laws of nature determine the probabilities of various futures and pasts rather than determining the future and past with certainty." (discussing a Many worlds interpretation).