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Fifty Challenging Problems in Probability with Solutions (Dover Books on Mathematics), by Frederick Mosteller
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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.
- Sales Rank: #80139 in eBooks
- Published on: 2012-04-26
- Released on: 2012-04-26
- Format: Kindle eBook
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
Most helpful customer reviews
156 of 160 people found the following review helpful.
A look at the essence of probability, at all levels
By Mary P. Campbell
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.
50 of 51 people found the following review helpful.
I passed my PhD qualifier because of this book!
By UNPINGCO
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.
41 of 41 people found the following review helpful.
useful, effective fun
By mcnicely
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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