IGCSE Maths: Probability Tree Diagrams and Conditional Probability (Student Book p.400) | IGCSE 数学：概率树形图与条件概率（学生用书第400页）

📚 IGCSE Maths: Probability Tree Diagrams and Conditional Probability | IGCSE 数学：概率树形图与条件概率

Probability tree diagrams are a powerful visual tool for calculating the probabilities of combined events. In IGCSE Mathematics, you need to draw, label and interpret tree diagrams for both independent and dependent events, and use them to solve conditional probability problems. This article is linked to the style of questions found around Student Book page 400.

概率树形图是计算组合事件概率的强大可视化工具。在 IGCSE 数学中，你需要会画、标记并解读独立事件和相关事件的树形图，并用它们解决条件概率问题。本文对应学生用书第 400 页附近的题型难度与知识点。

1. What Is a Probability Tree Diagram? | 什么是概率树形图？

A probability tree diagram shows all possible outcomes of a sequence of events as branches. Each branch is labelled with the probability of that outcome. The first set of branches shows the first event, and the next sets show the second event, third event, and so on.

概率树形图以分支形式展示一系列事件的所有可能结果。每个分支都标有该结果的概率。第一组分支表示第一个事件，后续各组表示第二个事件、第三个事件，以此类推。

You read a tree diagram from left to right. Each complete path through the diagram represents one combined outcome, such as ‘first red, then blue’.

从左到右阅读树形图。图中每一条完整路径代表一个组合结果，例如“先红后蓝”。

The key rule is that the probabilities on the branches from any single point must add up to 1.

关键规则是，从同一点出发的所有分支概率之和必须等于 1。

2. Independent Events: Repeating an Action with Replacement | 独立事件：有放回的重复试验

When the outcome of the first event does not affect the outcome of the second event, the events are independent. A common example is choosing a counter, replacing it, and then choosing again.

当第一个事件的结果不影响第二个事件的结果时，这两个事件是独立的。常见例子是抽取一个筹码，放回后再抽一次。

In an independent tree diagram, the probabilities on the second set of branches are exactly the same as the first set.

在独立事件的树形图中，第二组分支上的概率与第一组完全相同。

For example, a bag contains 5 red and 3 blue counters. One counter is taken, then replaced, and a second counter is taken.

例如，一个袋子里有 5 个红色和 3 个蓝色筹码。取出一个后放回，再取第二个。

P(R) = 5/8, P(B) = 3/8

To find the probability of two reds, multiply along the RR path.

要求两次都取到红球的概率，沿 RR 路径相乘。

P(RR) = 5/8 × 5/8 = 25/64

To find the probability of one red and one blue, you must add the probabilities of RB and BR because the order can differ.

要求一红一蓝的概率，

Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）