📚 Experimental and Theoretical Probability | 实验概率与理论概率
Probability is a branch of mathematics that measures the chance of an event happening. In KS3 you learn to describe, calculate and compare probabilities using words, fractions, decimals and percentages.
概率是数学的一个分支，用来衡量事件发生的可能性。在 KS3 阶段，你会学习用文字、分数、小数和百分比来描述、计算和比较概率。
Probability appears in daily life more often than you may think: weather reports, sports predictions, medical tests and board games all use the language of chance. A strong understanding of probability helps you make sense of risk and make better decisions.
概率在日常生活中的出现频率比你想象的还要高：天气预报、体育预测、医学检测和棋盘游戏都使用机会的语言。扎实地理解概率能帮助你理解风险并做出更好的决策。
1. What is Probability? | 什么是概率？
Probability measures how likely an event is to occur. It is always expressed as a number between 0 and 1, where 0 means impossible and 1 means certain.
概率衡量某个事件发生的可能性有多大。它总是用 0 到 1 之间的一个数来表示，其中 0 表示不可能发生，1 表示一定发生。
For example, the probability of the sun rising tomorrow is very close to 1, while the probability of rolling a 7 on an ordinary six-sided die is exactly 0.
例如，太阳明天升起的概率非常接近 1，而在普通六面骰子上掷出 7 点的概率恰好是 0。
Probabilities can be written as fractions such as ⅙, decimals such as 0.25, or percentages such as 50%. All of these are equivalent forms of the same measure.
概率可以写成分数如 ⅙、小数如 0.25 或百分比如 50%。这些都是同一度量的等价形式。
In mathematics we prefer to give probabilities as numbers rather than vague words, because numbers allow exact comparisons and calculations.
在数学中，我们更倾向于用数字而不是模糊的词语来表示概率，因为数字可以进行精确的比较和计算。
2. The Probability Scale | 概率尺度
The probability scale is a number line from 0 to 1. It helps you visualise how likely different events are.
概率尺度是一条从 0 到 1 的数轴。它帮助你直观地看出不同事件的可能性大小。
- 0 means impossible
- ½ means an even chance
- 1 means certain
0 表示不可能；½ 表示机会均等；1 表示必定发生。
Words like impossible, unlikely, even chance, likely and certain are often used in everyday language, but in mathematics we usually need a numerical value.
日常语言中常使用不可能、不太可能、机会均等、很可能和一定等词，但在数学中我们通常需要具体的数值。
For instance, drawing a red card from a standard deck has probability ½, so it sits exactly in the middle of the scale.
例如，从一副标准纸牌中抽出一张红色牌的概率是 ½，因此它恰好位于概率尺度的正中间。
An event with probability close to 0 is very unlikely, while an event with probability close to 1 is very likely. The scale gives you a quick way to judge how surprising an outcome is.
概率接近 0 的事件非常不可能发生，而概率接近 1 的事件非常可能发生。概率尺度能让你快速判断某个结果有多令人惊讶。
3. Theoretical Probability | 理论概率
Theoretical probability is calculated without doing an experiment. It assumes all outcomes are equally likely.
理论概率无需实验即可计算。它假设所有结果发生的可能性相等。
P(event) = number of favourable outcomes ÷ total number
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