Conditional Probability | 条件概率

📚 Conditional Probability | 条件概率

Conditional probability is one of the most important ideas in Edexcel A-Level Statistics. It measures how the chance of one event changes when we know that another event has happened. Understanding P(A | B) is essential for tree diagrams, two-way tables, independence tests and many real-world models such as disease testing and quality control.

条件概率是 Edexcel A-Level 统计部分最重要的概念之一。它衡量当我们已知另一个事件发生时，某个事件发生的概率如何变化。理解 P(A | B) 对树状图、双向表、独立性检验以及疾病检测、质量控制等实际模型都至关重要。

1. What is Conditional Probability? | 什么是条件概率？

Suppose A and B are events and P(B) > 0. The conditional probability of A given B is written P(A | B) and is read as “the probability of A given B”. It tells us how likely A is when we already know that B has occurred.

设 A 和 B 为两个事件，且 P(B) > 0。已知 B 发生条件下 A 的概率记作 P(A | B)，读作“在 B 发生的条件下 A 的概率”。它表示在已经知道 B 发生的情况下，A 发生的可能性有多大。

The formal definition is:

P(A | B) = P(A ∩ B) / P(B)

正式定义是：P(A | B)=P(A ∩ B)/P(B)。分母是已知事件 B 的概率，分子是 A 和 B 同时发生的概率。

Intuitively, B becomes the new sample space. We only consider outcomes in B, then ask what fraction of those outcomes also belong to A.

Published by TutorHao | A-Level Mathematics Revision Series | aleveler.com

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