MIT Massachusetts Institute of Technology

A Never-Fail Method for Probabilistic Problems

Enming Qing 
AP Economics, TOEFL and SAT instructor
Verakin High School of Chongqing
Chongqing, China

AP经济学, 托福和SAT教师

This lesson focuses on calculating the probability of random events. The main goal is to offer students some insights on probability through the understanding of sample space and use of the tree model. The lesson lasts approximately 50 minutes. To conduct this course, the instructor needs to prepare a spinning wheel, which could be self-made, and also some prizes for those lucky winners in the spinning wheel game. Regarding the student activities, here are a few suggestions: 1. In the actual spinning wheel game, teachers can change the number of participants and the ratio of boys to girls as well. 2. When drawing the tree models, teachers could explain the branches and the nodes to the students, show students the steps of drawing a tree model and ask them to practice for several times to help familiarize them with tree models. 3. Teachers should encourage students to figure out different ways to calculate probability, such as the empirical way.

这节课是关于如何计算随机事件发生的概率。主要学习目标是:学生可以通过学习概率的基本概念(样本容量,独立事件,相互排斥 ),画树状图,利用条件概率来计算出随机事件发生的概率。希望通过这节课,激发学生对于概率学习的兴趣。这节课的时长为40分钟到50分钟,一节课左右。完成这节课,尤其是搞小组活动,需要的工具有一个轮盘(可以自己来制作,轮盘带有指针就足够了),几份(数量根据游戏参与人数来定)奖品发给做游戏被抽中的学生。关于学生活动,有以下建议。比如:①做转盘游戏的时候,可以增加学生参与人数,男女比例可以根据班上实际情况来调整。②画树状图的时候,老师可以给学生先演示几遍。③激发学生想出其他计算概率的方法,比如运用统计学知识,让学生把这个转盘游戏玩很多遍,每次结果纪录下来,做一个统计,根据实际的数据来估算一下概率是多少。

Enming received her bachelor’s degree in Mathematics and master’s degree in Financial Engineering from the Johns Hopkins University. Since graduation, she has worked with overseas study programs. She has taught AP Economics for four years, and TOEFL and SAT for five years. More than twenty of her students have been admitted to the world’s top 50 universities. Read more at:

我大学的专业是数学。之后,我在约翰霍普金斯大学获得了金融工程硕士学位。硕士毕业以后, 我一直从事出国留学考试培训的教学工作,教授了AP经济学课程4年,托福和SAT课程5年。我非常热爱自己的教育教学工作,这几年培养了二十几名被世界五十强大学录取的优秀学生

This site by Khan Academy provides a comprehensive introduction to probability.

This resource, sponsored by Math Goodies, presents a series of activities for introducing students to the subject of probability.

This Wikipedia resource discusses the concept of Independence in Probability.

This Wikipedia resource discusses the concept of Collectively Exhaustive Events in Probability Theory.

This Wikipedia resource discusses the concept of Mutual Exclusivity in Probability Theory.

This url is for a BLOSSOMS lesson that also introduces Probability.

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