This site contains an interactive applet illustrating the Monty Hall problem as well as a page describing the history of the Monty Hall paradox and a comprehensive proof of its non-intuitive solution.
Type of Material:
In class demonstration or student reference.
A Java-enabled browser.
Identify Major Learning Goals:
The major learning goal of this site is to provide visual and numerical illustrations to the Monty Hall paradox.
Target Student Population:
Any student familiar with the empirical definition of probability.
Prerequisite Knowledge or Skills:
Basic understanding of probability.
This site contains a very vivid simulation of the Monty Hall problem, a puzzle involving probability loosely based on the TV game show Let's Make a Deal. The problem is also called the Monty Hall paradox in the sense that the solution is counterintuitive although the problem does not yield a logical contradiction. Using a random generator, a site visitor is allowed to play the simulation which results in a tabulation of statistical data based on the number of times the simulation has been played. While the data itself is empirically convincing, the visitor can read a linked page containing the explanation and a rigorous proof.
While the given explanation/proof of the correct solution is visually appealing and quite adequate, the more mathematically inclined visitors might prefer the kind of proof provided at http://www.amstat.org/publications/jse/v13n2/carlton.html. (See problems #3.)
Potential Effectiveness as a Teaching Tool
This site is perfect as a one-time in-class demonstration or as a part of a student project in an introductory probability and statistics course. Being a game in nature, it helps to develop a thorough understanding of the definition of probability and gives an introduction to the type of logic used in proofs of many probability problems.
Ease of Use for Both Students and Faculty
The site is extremely easy to use. All it takes to start the applet is two clicks with the mouse.
Concerns: The navigation structure of the site is a little too primitive. In particular, the only way one can get to the explanation page is by playing the applet.
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