Fifty Challenging Problems in Probability with SolutionsCan 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. |
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average number ballot binomial binomial distribution Birthday Pairings birthmate problem Bold Play cards chance of winning choose the first Choosing the Largest chord Chuck-a-Luck correct decision deck dice are rolled draw equal Erewhon Euler’s example expected number factory false coins figure final find first throw fraction gambler Gambler’s Ruin gambling geometric series gives infinite Isaac Newton largest dowry length locomotives logarithms Matching Pennies mean number Nathan Jacobson natural logarithms needle number of matches number of plays number of returns optimum origin Paradise particle returns pay to play penny player Poisson distribution Poisson problem position principle of symmetry prize probability of exactly probability of winning PWSA Quadratic Equations radius Random Number random walk randomly released sample Samuel Pepys segment sequence slips Solution square step Stirling’s approximation strategy toss total number unit interval unit stake vertical rulings warder says white balls zero