📚 Probability: Single Events and Expected Frequency | 概率：单次事件与期望频数
In KS3 mathematics, probability is the study of chance. It helps us describe how likely an event is to happen, using numbers between 0 and 1. This article reviews key ideas including the probability scale, equally likely outcomes, complementary events, sample space diagrams, experimental probability and expected frequency. Worked examples and tips are included to support Cambridge Checkpoint preparation.
在 KS3 数学中，概率研究的是事件发生的可能性。它帮助我们用一个介于 0 和 1 之间的数来描述一个事件发生的把握有多大。本文回顾概率标度、等可能结果、对立事件、样本空间图、实验概率和期望频数等重点概念，并提供例题与技巧，帮助备战剑桥 Checkpoint 考试。
1. The Probability Scale and Key Words | 概率标度与关键术语
Probability is a measure of how likely an event is to happen. It always takes a value between 0 and 1, where 0 means impossible and 1 means certain.
概率是衡量一个事件发生可能性大小的指标。它的值总是在 0 和 1 之间，其中 0 表示不可能，1 表示必然。
On the scale, an event with probability 1/2 has an even chance. Events with probability less than 1/2 are unlikely, and events with probability greater than 1/2 are likely.
在标度上，概率为 1/2 的事件具有均等机会。概率小于 1/2 的事件不太可能发生，概率大于 1/2 的事件很可能发生。
Key words:
- Impossible - probability 0 | 不可能 - 概率 0
- Unlikely - probability less than 1/2 | 不太可能 - 概率小于 1/2
- Even chance - probability 1/2 | 均等机会 - 概率 1/2
- Likely - probability greater than 1/2 | 很可能 - 概率大于 1/2
- Certain - probability 1 | 必然 - 概率 1
2. Basic Probability Formula for Equally Likely Outcomes | 等可能结果的基本概率公式
When all outcomes are equally likely, we can find the probability of an event by counting favourable outcomes and dividing by the total number of outcomes.
当所有结果可能性相同时，我们可以用有利结果的数量除以所有可能结果的总数来求事件的概率。
P(event) = number of favourable outcomes ÷ total number of outcomes
For example, when a fair six-sided dice is rolled, each of the six outcomes has the same chance. The probability of rolling a 3 is 1/6 because there is one favourable outcome and six possible outcomes.
例如，掷一个均匀的六面骰子时，六种结果中每一种出现的机会相同。掷出 3 点的概率是 1/6，因为只有 1 个有利结果，共有 6 个可能结果。
This formula only works if every outcome is equally likely. If a dice is biased, we cannot simply count outcomes.
这个公式只在每个结果等可能时成立。如果骰子有偏，就不能简单地数结果。
3. Worked Example: Coloured Balls | 例题：彩色球
A bag contains 3 red balls, 5 blue balls and 2 green balls. A ball is taken at random. Find the probability that the ball is blue.
一个袋子里有 3 个红球、5 个蓝球和 2 个绿球。随机
Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图