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Fifty Challenging Problems in Probability with Solutions (Dover Books on Mathematics) Paperback – May 1, 1987

by Frederick Mosteller (Author)

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Can you solve the problem of "The Unfair Subway"?

Marvin gets off work at random times between 3 and 5 p.m. His mother lives uptown, his girlfriend downtown. He takes the first subway that comes in either direction and eats dinner with the one he is delivered to. His mother complains that he never comes to see her, but he says she has a 50-50 chance. He has had dinner with her twice in the last 20 working days. Explain.

Marvin's adventures in probability are one of the fifty intriguing puzzles that illustrate both elementary ad advanced aspects of probability, each problem designed to challenge the mathematically inclined. From "The Flippant Juror" and "The Prisoner's Dilemma" to "The Cliffhanger" and "The Clumsy Chemist," they provide an ideal supplement for all who enjoy the stimulating fun of mathematics.

Professor Frederick Mosteller, who teaches statistics at Harvard University, has chosen the problems for originality, general interest, or because they demonstrate valuable techniques. In addition, the problems are graded as to difficulty and many have considerable stature. Indeed, one has "enlivened the research lives of many excellent mathematicians." Detailed solutions are included. There is every probability you'll need at least a few of them.

Fifty Challenging Problems in Probability with Solutions (Dover Books on Mathematics)

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Product Details

Series: Dover Books on Mathematics
Paperback: 96 pages
Publisher: Dover Publications; Revised ed. edition (May 1, 1987)
Language: English
ISBN-10: 0486653552
ISBN-13: 978-0486653556
Product Dimensions: 0.2 x 5.5 x 8.2 inches
Shipping Weight: 4.8 ounces (View shipping rates and policies)
Average Customer Review: 4.3 out of 5 stars See all reviews (40 customer reviews)
Amazon Best Sellers Rank: #24,449 in Books (See Top 100 in Books)
- #69 in Books > Science & Math > Mathematics > Applied > Probability & Statistics

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4.3 out of 5 stars

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Top Customer Reviews

A look at the essence of probability, at all levels

ByMary P. Campbellon July 3, 2001

Format: Paperback

If Mosteller hadn't included the solutions, this would have been a short book indeed -- 56 problems simply stated in 14 pages. You'll soon find, however, that some problems, which are the shortest to set up, take a great deal of brainpower. It starts innocently enough - some simple-sounding problems on socks in drawers, flipping coins, and rolling dice. Soon enough, you end up with paper black with numbers and pictures of a flipping coin (how thick does a coin need to be so that it lands on its =side= with probability 1/3?) If you get drawn in deep (as I did), you may even wonder what probability really means.
Some of the problems are classic, such as the problem of how many people would it take for the probability that at least two of them have the same birthday is greater than a half (I'll give this answer away: 23. But do you know why?) One of the dice problems actually recalls the history of the development of probability as a separate mathematical field -- problem #19, involving dice bets that Samuel Pepys asked Isaac Newton to figure out. Some of the problems are simply openers for entire vistas in probability - avoid problems #51 and #52 if you wish to not become enmeshed in concerns of random walks (remember that one of Einstein's earliest papers was on Brownian motion - a molecular random walk.) I used problem #25, which deal with "random chords on a circle", to explore this classic probability paradox - I've ended up with three different figures, all of which seem plausible! It gets deep to what one means by "random chord".
This book, though so thin, is inexhaustible in spawning disturbing questions about probability; even more useful is that there are questions for people at =any= level of knowledge of probability. Those who wish to think about "counting" problems (like those involving rolling dice, or pulling balls out of urns) will find those here. Those who have an interest in continuous probability will find problems which will interest them. And those old probability pros who ponder the essence of chance will find meat for some productive chewing.

44 comments 156 people found this helpful. Was this review helpful to you?YesNo

I passed my PhD qualifier because of this book!

ByUNPINGCOon June 12, 2000

Format: Paperback

Excellent selection of problems and very explanatory and detailed solutions. This gets to the ideas behind many of the popular methods in probability, like maximum likelihood. The concepts are given centerstage and provide insights on "how to think" about many problems in probability.

0Comment 50 people found this helpful. Was this review helpful to you?YesNo

useful, effective fun

Bymcnicelyon February 1, 2002

Format: PaperbackVerified Purchase

Working through the colorful problems in this book is a great way to (re)learn and apply basic probability principles. There is a great deal of independence between problem so you are never quite sure how tough or easy the next one will be. On the other hand, several of the problems are clearly follow-ons that allow the exploration or expansion of some of the more interesting issues.
Though I've worked through the problems a couple of times, I bought a replacement copy when my original was "permanently borrowed" from my desk at work.

0Comment 41 people found this helpful. Was this review helpful to you?YesNo

Enjoyable

ByJames M. Cargalon October 13, 2000

Format: Paperback

There are other books on problems in probablity. However, this book has problems that are interesting (often counterintuitive). They are well written as are the solutions. Much of the book is at the pre-calculus level but the problems are not trivial; neither are they arcane. Many teachers use this book as a source of problems. It is great for all students of probability.

0Comment 18 people found this helpful. Was this review helpful to you?YesNo

detailed instructive solutions

ByKen Braithwaiteon May 31, 2001

Format: Paperback

The problems range from easy to incredibly hard. They are chosen to illustrate points or techniques. Many also have a touch of humour. You will learn a lot from this book. Few theorems are mentioned! Fun, cheap, instructive, amusing.

0Comment 16 people found this helpful. Was this review helpful to you?YesNo

Probability taken to the next level

ByBlakeobeanson December 31, 2011

Format: PaperbackVerified Purchase

I enjoy solving probability puzzles. I considered myself to be pretty good- I could solve any problem that the GRE practice exams could throw my way. Until I opened this book.

This book takes off where I ended up. The first problem is a variation on the "reach into a bag" probability problem. (Q: You reach into a drawer with red socks and black socks, and the probability of drawing 2 red socks is P=0.5. What is the minimum number of both colored socks?)

You won't find the typical probability problems that can be quickly solved with basic combinatorial analysis or the Bernoulli Coefficient. You'll find variations and completely new worlds of probability. The explanations are thorough but succinct, and will arm you with a new skill set for solving such problems.

There's no other book like it on Amazon, and for $7...

Comparable to Huff's "How to Lie with Statistics" in its originality and straight-forwardness.

0Comment 10 people found this helpful. Was this review helpful to you?YesNo

Challenging, sometimes lacking explanation

ByTyler Ferraroon December 15, 2011

Format: PaperbackVerified Purchase

I got this book because I enjoy programming challenges, probability and logical reasoning and wanted to strengthen my math skills. With that said, I struggled right out of the gate with the problems. I understood the problems and was able to solve them on my own but when reading the solution and trying to follow through with the mathematical approach I found myself completely confused. The math isn't always intuitive and the author makes a few leaps during his explanations that not only could I not follow, but I couldn't recreate in my own math. This was frustrating to no end and I still don't understand a lot of the math he used to get to his solutions. It's a great book if you like challenges and probability and those who have a stronger math background than myself might enjoy this book a lot. However, for me this book just didn't quite make the cut and I'd really enjoy one with a better set of answers and explanations to go with.

0Comment 12 people found this helpful. Was this review helpful to you?YesNo

Good Distraction

ByDavid C Hunton July 10, 2001

Format: Paperback

Even if you are not a big probability fan, you are more than likely to find something enjoyable in this book. Some of the problems are wasy, some are hard, and some are just strange, but it makes for a very entertaining diversion for the mathematically inclined.

0Comment 10 people found this helpful. Was this review helpful to you?YesNo

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Most Recent Customer Reviews

this is one of the best purchases I've ever made

Outstanding book. For the money, this is one of the best purchases I've ever made.

Published 3 months ago by Customer_D

some difficult; great for when one is stuck in traffic

A particularly nice puzzle book for reflecting on when stuck in traffic.

Published 3 months ago by Geo Stalker

It is indeed challenging.

Challenging and thought provoking. It took me a while to get what "erewhon" was ... useful for all sorts of math and science.

Published 6 months ago by Amazon Customer

Two Stars

Most questions are too simple

Published 7 months ago by jinyi sun

This book is ok for a coffee break exercise. If that's why you want to buy it then you may stop reading.Read more

Published 10 months ago by Maksym Zavershynskyi

Great read, the author provides concise

Great read, the author provides concise, beautiful layout for the problems and a lot of hand holding for all the knots and bolts needed to build intuition.

Published 11 months ago by Siwei Wang

Really fun. Not the most challenging in the world

Really fun. Not the most challenging in the world, but really useful for prepping for quant interviews and for refreshing basic probability skills.

Published 1 year ago by S E

The author does a really good job on presenting a comprehensive way of understanding the ...

It is what it is... A book with interesting problems in statistics. And that's really all it is. The author does a really good job on presenting a comprehensive way of...Read more

Published 1 year ago by Benjamin Evans

Five Stars

Fun book.

Published 1 year ago by J.E.R

Five Stars

great brain exercise

Published 1 year ago by Ellen Brainard

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Fifty Challenging Problems in Probability with Solutions (Dover Books on Mathematics) Paperback – May 1, 1987

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