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The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brainteaser

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The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brainteaser Cover

ISBN13: 9780195367898
ISBN10: 0195367898
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Synopses & Reviews

Publisher Comments:

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.

About the Author

Jason Rosenhouse is an Associate Professor of Mathematics at James Madison University in Virginia.

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Peter Flom, May 2, 2009 (view all comments by Peter Flom)
What's in this book?

It's about the Monty Hall problem, the classic version of which is:


You are on a game show. You are presented with three doors.
Behind one of them is a car, behind the other two are goats. You
get to choose a door. But before you open it, the host (Monty Hall),
who knows where the car is, opens one of the other doors. He always
opens a door with a goat. If both of the unchosen doors have goats,
he picks one at random. The car was placed randomly, with 1/3 chance
for each door.

You are then offered a chance to change doors, or stick with your
choice.

What should you do?


Here's the table of contents:
1. Ancestral Monty
has considerable detail about the origins of the problem and the huge outcry when vos Savant published the right answer. This is presented in a light and humorous way, showing how the intuition of many people is completely wrong.

2. Classical Monty
covers the problem above, giving reasons based on intuition, as well as on formal probability.


3. Bayesian Monty
covers a variation in which Monty does not know which door has the car, and introduces Bayesian notions.

4. Progressive Monty
is by far the most technical in the book; it covers many variations on the problem, and teaches a lot of probability theory.

5. Miscellaneous Monty
covers some additional variations on the problem

6. Cognitive Monty
discusses why our intuition is so wrong on this problem and others, and reviews research into this.

7. Philosophical Monty
discusses philosophical issues in probability

8. Final Monty
sums up.
Who should read the book?

I think it has a couple audiences. First, if you are taking a formal probability course at university, this could be a good backup to your text. OTOH, if you are *teaching* such a course, you could use this as a main text (I've never seen a probability text that is this much fun to read). A course based on this book would cover a lot of the ground of a one-semester intro to probability course.

Among the general population, I think this book could be read in two ways: First, you could read chapters 1, 2, 6, 7, and 8, and either skip 3, 4, and 5 or skim them. (Chapter 4, in particular, will be heavy going). Second, if you want to learn probability theory, you could read the whole book. In this case, you'll want to read it more like a text book.
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Product Details

ISBN:
9780195367898
Author:
Rosenhouse, Jason
Publisher:
Oxford University Press, USA
Author:
null, Jason
Subject:
Probability & Statistics - General
Subject:
Statistics
Subject:
General Mathematics
Subject:
Mathematical recreations
Subject:
Monty Hall problem
Subject:
History -- Philosophy.
Subject:
Mathematics | Probability
Subject:
Mathematics | Probability & Statistics
Subject:
Mathematics -- History.
Edition Description:
The Remarkable
Publication Date:
20090631
Binding:
HARDCOVER
Grade Level:
General/trade
Language:
English
Illustrations:
2 line (B/W)
Pages:
208
Dimensions:
6.3 x 9.2 x 0.8 in 0.9 lb

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