Fifty Challenging Problems in Probability with Solutions

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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. Feature 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.

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s "Though we often hear that data can speak for themselves, their voices can be soft and sly." — Frederick Mosteller Table Of Content The sock drawer Successive wins The flippant juror Trials until first success Coin in square Chuck-a-luck Curing the compulsive gambler Perfect bridge hand Craps An experiment in personal taste for mone Silent cooperation Quo vadis? The prisoner's dilemma "Collecting coupons, including Euler's approximation for harmonic sums" The theater row Will second-best be runner-up? Twin knights "An even split at coin tossing, including Stirling's approximation" Isaac Newton helps Samuel Pepys The three-cornered duel Should you sample with or without replacement? The ballot box Ties in matching pennies The unfair subwa Lengths of random chords The hurried duelers Catching the cautious counterfeiter "Catching the greedy counterfeiter, including the Poisson distribution" Moldy gelation Evening the sales Birthday pairings Finding your birthmate Relating the birthday pairings and birthmate problems Birthday holidays The cliff-hanger Gambler's ruin Bold play vs. cautious play The thick coin Digression: A note on the principle of symmetry when points are dropped on a line The clumsy chemist The first ace The locomotive problem The little end of the stick The broken bar Winning an unfair game Average number of matches Probabilities of matches Choosing the largest dowry Choosing the largest random number Doubling your accuracy Random quadratic equations Two-dimensional random walk Three-dimensional random walk Buffon's needle Buffon's needle with horizontal and vertical rulings Long needles56. Molina's urns