The Monty Hall Problem

That is, each triple in our sample space will have the following form: (Your initial choice, The door Monty opens, ... To answer that question, let us simplify our problem by assuming you always choose door number one initially.

The Monty Hall Problem

Mathematicians call it the Monty Hall Problem, and it is one of the most interesting mathematical brain teasers of recent times. Imagine that you face three doors, behind one of which is a prize. You choose one but do not open it. The host--call him Monty Hall--opens a different door, always choosing one he knows to be empty. Left with two doors, will you do better by sticking with your first choice, or by switching to the other remaining door? 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. As Rosenhouse demonstrates, the Monty Hall Problem illuminates fundamental mathematical issues and has abiding philosophical implications. Perhaps most important, he writes, the problem opens a window on our cognitive difficulties in reasoning about uncertainty.

More Books:

The Monty Hall Problem
Language: en
Pages: 208
Authors: Jason Rosenhouse
Categories: Mathematics
Type: BOOK - Published: 2009-06-04 - Publisher: Oxford University Press

Mathematicians call it the Monty Hall Problem, and it is one of the most interesting mathematical brain teasers of recent times. Imagine that you face three doors, behind one of which is a prize. You choose one but do not open it. The host--call him Monty Hall--opens a different door,
The Monty Hall Problem & Other Puzzles
Language: en
Pages: 128
Authors: Ivan Moscovich
Categories: Puzzles
Type: BOOK - Published: 2005 - Publisher: Robson Books Limited

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
Probability, Choice, and Reason
Language: en
Pages: 310
Authors: Leighton Vaughan Williams
Categories: Mathematics
Type: BOOK - Published: 2021-09-15 - Publisher: CRC Press

Much of our thinking is flawed because it is based on faulty intuition. By using the framework and tools of probability and statistics, we can overcome this to provide solutions to many real-world problems and paradoxes. We show how to do this, and find answers that are frequently very contrary
Proceedings of the Twentieth Annual Conference of the Cognitive Science Society
Language: en
Pages: 1284
Authors: Morton Ann Gernsbacher, Sharon J. Derry
Categories: Psychology
Type: BOOK - Published: 1998 - Publisher: Psychology Press

This volume of proceedings contains papers, posters, and summaries of symposia presented at the leading conference that brings cognitive scientists together to discuss issues of theoretical and applied concern. For researchers and educators in the field.
Martin Gardner in the Twenty-First Century
Language: en
Pages: 297
Authors: Michael Henle
Categories: Education
Type: BOOK - Published: 2012-12-31 - Publisher: American Mathematical Soc.

Martin Gardner enormously expanded the field of recreational mathematics with the Mathematical Games columns he wrote for Scientific American for over 25 years and the more than 70 books he published. He also had a long relationship with the Mathematical Association of America, publishing articles in MAA journals right up