 # 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.

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: http://www.ams.jhu.edu/~eqing/CV.html Teacher's Guide in Chinese (PDF format) Teacher's Guide in Chinese (Word format) Teacher's Guide in English (PDF format) Teacher's Guide in English (Word format) Homework Probability Graph (PDF format) Tree Model of Spin Wheel Game (PDF format) Tree Model of Homework Problem (PDF format)

This site by Khan Academy provides a comprehensive introduction to probability.
https://www.khanacademy.org/math/probability/independent-dependent-probability

This resource, sponsored by Math Goodies, presents a series of activities for introducing students to the subject of probability.
http://www.mathgoodies.com/lessons/vol6/intro_probability.html

This Wikipedia resource discusses the concept of Independence in Probability.
https://en.wikipedia.org/wiki/Independence_(probability_theory)

This Wikipedia resource discusses the concept of Collectively Exhaustive Events in Probability Theory.
https://en.wikipedia.org/wiki/Collectively_exhaustive_events

This Wikipedia resource discusses the concept of Mutual Exclusivity in Probability Theory.
https://en.wikipedia.org/wiki/Mutual_exclusivity

This url is for a BLOSSOMS lesson that also introduces Probability.
http://blossoms.mit.edu/videos/lessons/monty_hall_problem_or_how_outsmart_game_show_and_win_car Written Transcript of this video lesson in Chinese (PDF format) Written Transcript of this video lesson in Chinese (Word format)
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