# 概率

(由機會率跳轉過嚟)

## 基礎

• 啲人一般會用「${\displaystyle P(A)}$ 」或者「${\displaystyle \Pr(A)}$ 」嚟代表「${\displaystyle A}$  發生嘅概率」，
• 而一場實驗嘅結果（${\displaystyle f(i)}$ ）可以用噉嘅方式表達[4]
${\displaystyle f(i)={\begin{cases}p_{1}&{\text{if }}i=1,\\p_{2}&{\text{if }}i=2,\\p_{3}&{\text{if }}i=3,\\...\end{cases}}}$
${\displaystyle i=1}$  嘅概率係 ${\displaystyle p_{1}}$ 」、「${\displaystyle i=2}$  嘅概率係 ${\displaystyle p_{2}}$ 」... 呀噉；${\displaystyle i}$  可以想像成（例如）「擲骰仔得到嘅數」。

## 研究史

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

## 引述

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).