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

4.3 out of 5 stars 36 customer reviews

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Editorial Reviews

From the Back Cover

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.

About the Author

Charles Frederick Mosteller ( 1916–2006) was one of the eminent statisticians of the 20th century. He was the founding chairman of Harvard's Statistics department. Dr. Mosteller wrote more than 50 books and more than 350 papers, with over 200 coauthors.

Frederick Mosteller: Harvard Man
Frederick Mosteller (1916–2006) founded Harvard University's Department of Statistics and served as its first chairman from 1957 until 1969 and again for several years in the 1970s. He was the author or co-author of more than 350 scholarly papers and more than 50 books, including one of the most popular books in his field, first published in 1965 and reprinted by Dover in 1987, Fifty Challenging Problems in Probability with Solutions.

Mosteller's work was wide-ranging: He used statistical analysis of written works to prove that James Madison was the author of several of the Federalist papers whose authorship was in dispute. With then–Harvard professor and later Senator Daniel P. Moynihan, he studied what would be the most effective way of helping students from impoverished families do better in school — their answer: to improve income levels rather than to simply spend on schools. Later, his analysis of the importance to learning of smaller class sizes buttressed the Clinton Administration's initiative to hire 100,000 teachers. And, as far back as the 1940s, Mosteller composed an early statistical analysis of baseball: After his team, the Boston Red Sox, lost the 1946 World Series, he demonstrated that luck plays an enhanced role in a short series, even for a strong team.

In the Author's Own Words:
"Though we often hear that data can speak for themselves, their voices can be soft and sly." — Frederick Mosteller

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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 (36 customer reviews)
  • Amazon Best Sellers Rank: #83,734 in Books (See Top 100 in Books)

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Customer Reviews

Top Customer Reviews

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.
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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.
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Format: Paperback Verified 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.
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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.
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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.
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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.
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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.
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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.
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Fifty Challenging Problems in Probability with Solutions (Dover Books on Mathematics)
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