The main objective of this lesson is to motivate students’ thoughts and get them excited about some probability concepts. The aim is to present probability theory in as simple a manner as possible. It is hoped that students will learn that probability theory is a basic tool for handling an uncertain future and making a decision. The prerequisites necessary for this lesson include basic algebra and knowledge of the definitions of the following terms: sample space; events; probability; the multiplicative law of probability; marginal, conditional, and joint probabilities. The video part of this lesson will take 30 minutes, and the necessary supplies include: a poster showing the 3-door problem; empty envelopes as well as a monetary bill (for example, a $20 bill); and a simple tree (one stem with two branches, other two stems with one branch for each). Examples of in-class activities for breaks are: conducting the real-life three-envelope experiment when the student does not change his/her mind and conducting the same experiment when the student does change his/her mind. Students will also learn to develop and work with probability trees.
Mohammad Z. Raqab is professor of statistics at the University of Jordan. He completed his B.Sc. (1981) in mathematics at the University of Jordan, M. Sc. (1989) and PhD (1992) in statistics at Ohio State University, Ohio State, USA. His areas of interests: Statistical Models Involving Ordered Random Variables, Optimal Evaluations of Statistical Functionals, Biostatistical Applications on Censoring Data, Reliability Theory, Intensive Computer Studies, Information Technology and E-learning.
Additional Online Resources
Wolfram MathWorld: Monty Hall Problem
This site, provided by Wolfram MathWorld, presents an introduction to the Monty Hall Problem along with demonstration simulations of this problem, the Monty Hall Paradox and standardized and generalized versions of the Monty Hall Problem.
Shodor: Advanced Monty Hall
This site, provided by Shodor, allows the user to simulate the Monty Hall Game with up to 100 doors in which the user chooses a door, and then all but one door is opened to reveal a stinking pig. The player must then decide to stick with the original choice or change.