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

Frederick Mosteller (Author)

Book Description

Publication Date: May 1, 1987 | Series: Dover Books on Mathematics

Remarkable selection of puzzlers, graded in difficulty, that illustrate both elementary and advanced aspects of probability. Selected for originality, general interest, or because they demonstrate valuable techniques, the problems are ideal as a supplement to courses in probability or statistics, or as stimulating recreation for the mathematically minded. Detailed solutions. Illustrated.

Product Details

• Paperback: 88 pages
• Publisher: Dover Publications; ?over 0-486-65355-2 edition (May 1, 1987)
• Language: English
• ISBN-10: 0486653552
• ISBN-13: 978-0486653556
• Product Dimensions: 0.2 x 0.2 x 8.5 inches
• Shipping Weight: 4.8 ounces (View shipping rates and policies)
• Average Customer Review: 4.3 out of 5 stars  See all reviews (27 customer reviews)
• Amazon Best Sellers Rank: #13,434 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

140 of 144 people found the following review helpful

5.0 out of 5 stars A look at the essence of probability, at all levels July 3, 2001

By Mary P. Campbell

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.

36 of 36 people found the following review helpful

5.0 out of 5 stars useful, effective fun February 1, 2002

By mcnicely

Format:Paperback|Amazon 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.

43 of 44 people found the following review helpful

5.0 out of 5 stars I passed my PhD qualifier because of this book! June 12, 2000

By UNPINGCO

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.