The Monty Hall Problem

This short book explores the Monty Hall dilemma, a well known mathematical puzzle. The original problem, the controversy surrounding it and its solution are discussed. Further, the boundaries of the problem are expanded to consider prior knowledge and host intention. This book should be of interest to those who enjoy problem solving.

In this light-hearted yet ultimately serious book, Jason Rosenhouse explores the history of this fascinating puzzle. Using a minimum of mathematics (and none at all for much of the book), he shows how the problem has fascinated philosophers, psychologists, and many others, and examines the many variations that have appeared over the years.

Puzzlers will feel fit to be tied - Dog Tied: If Fido is tied to a 10-foot-long rope, and his bone is 15 feet away, how is it possible that he can reach and enjoy his bone without breaking or stretching the rope? (And yes - the rope IS tied to something.) There's fun in finding the answer to this and other cool number-based problems. Dust off your mathematics and get solving. The intriguing enigmas include questions on interstellar communications, ancient geometry (Pythagoras and Plato), and even traffic patterns in gridlock city. Or play the grasshopper jumping game. It's all fascinating.

This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered - either by one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geometry of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of Hölder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics.

"Parade" magazine's resident genius compiles the best of her question-and-answer column that logically tackles the mysteries of the universe, brainteasers, and unique insights

A cognitive illusion occurs when the obvious answer to a thought question turns out to be incorrect. Psychological reality conflicts with objective reality. The Monty Hall Dilemma is a cognitive illusion par excellence originating in the "Let's Make a Deal" television game show in which a contestant selects one of three doors hoping that it hides the grand prize (like a new car!). After an initial guess has been made, host Monty Hall reveals a consolation prize (like a goat!) behind one of the other doors. The contestant's dilemma is whether to stay with the first choice or switch to the remaining unchosen door. Popular PARADE magazine columnist, Marilyn vos Savant, writing about the Monty Hall dilemma, received thousands of letters from readers most of whom contested her surprising solution to this dilemma. Knowing about cognitive illusions in general (several are presented here) and the Monty Hall Dilemma in particular should alert readers to the possibility that ordinary reasoning and common sense don't always apply even though people have a tendency to stick with their initial hunches.

This guide provides a wide-ranging selection of illuminating, informative and entertaining problems, together with their solution. Topics include modelling and many applications of probability theory.

Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.