Laws of Probability | 概率法则

📚 Laws of Probability | 概率法则

Probability is the mathematical language of uncertainty. For IGCSE Edexcel Mathematics, mastering the laws of probability enables you to analyse random experiments, predict outcomes, and solve real-world problems systematically. This revision guide covers all the essential probability rules you need for your examination.

概率是描述不确定性的数学语言。对于 IGCSE Edexcel 数学考试，掌握概率法则能够帮助你分析随机试验、预测结果，并系统地解决现实世界中的问题。本复习指南涵盖了考试所需的所有核心概率规则。

1. The Probability Scale | 概率尺度

Every probability is a number between 0 and 1 inclusive. A probability of 0 means an event is impossible; a probability of 1 means an event is certain. Probabilities can be written as fractions, decimals, or percentages.

每个概率都是介于 0 和 1 之间的数（包含 0 和 1）。概率为 0 表示事件不可能发生；概率为 1 表示事件必然发生。概率可以用分数、小数或百分数表示。

When all outcomes of an experiment are equally likely, the probability of an event A is:

当试验的所有结果等可能发生时，事件 A 的概率为：

P(A) = number of favourable outcomes ÷ total number of possible outcomes

P(A) = 有利结果数 ÷ 所有可能结果总数

For example, when rolling a fair die, the sample space is {1, 2, 3, 4, 5, 6}, so P(rolling a 4) = 1 ÷ 6 = ⅙. Similarly, P(rolling an even number) = 3 ÷ 6 = ½.

例如，掷一枚均匀骰子时，样本空间为 {1, 2, 3, 4, 5, 6}，所以 P(掷出 4) = 1 ÷ 6 = ⅙。同样地，P(掷出偶数) = 3 ÷ 6 = ½。

2. Sample Spaces and Events | 样本空间与事件

The sample space is the set of all possible outcomes of an experiment. An event is any subset of the sample space. Listing the sample space helps you count outcomes systematically, especially when combined events are involved.

样本空间是试验所有可能结果的集合。事件是样本空间的任意子集。列出样本空间有助于系统地计数结果，尤其是在涉及组合事件时。

Consider tossing two fair coins. The sample space is:

考虑抛掷两枚均匀硬币。样本空间为：

There are 4 equally likely outcomes. Therefore, P(one head and one tail) = 2 ÷ 4 = ½, since the outcomes HT and TH are both favourable.

共有 4 个等可能结果。因此，P(一正一反) = 2 ÷ 4 = ½，因为 HT 和 TH 都是有利结果。

3. Complementary Events | 互补事件

The complement of event A, written as A’ or “not A”, is the event that A does not occur. The complement rule states:

事件 A 的互补事件，记为 A’ 或”非 A”，表示事件 A 不发生。互补法则为：

P(not A) = 1 − P(A)Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com

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