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Rezension bezieht sich auf: Fifty challenging problems in probability with solutions (Taschenbuch)
Here is a worthwhile collection, presented with a good dose of humour, of brainteasers for those who enjoy solving mathematical problems without the burden of much theory. The booklet presents 56 (and not just 50) problems from probability. All problems can be solved without recourse to books on the subject provided the reader is familiar with the mathematical notion of probability and understands how to compute probabilities for conjoint events. Some problems require elementary geometric abilities. Understanding binomial coefficients, for example, falls under the nice-to-have abilities which are not prerequisite.
The problems come in various degrees of difficulty, and they try to highlight different aspects of likelihood that are not usually encountered in textbooks on theory. Among them are the 'problems without structure' which show that our intuitive notion of likelihood is much richer than what is formalized in mathematics (Think about what two strangers to NY, personally unknown to each other and with no means of communicating, should do to maximize the likelihood of them finding each other in this town on a given day at an appointed hour). Some problems require essentially no computation (After work, a chap takes whatever subway on a north-south line arrives first to go either see his mother in the North or his fiancée in the South at night. He only gets to see his mother on two out of 20 days on average. How can that be?). There are also a few of the classical problems (prisoner's dilemma, the three cornered duel, the length of random cords) which no good collection can miss. Most of the other problems involve the usual paraphernalia like coins, ballot boxes and cards.
The solutions provided with the problems are explained at great length. The author always starts with showing how one arrives by the solution trough elementary reasoning, and only then will he proceed to cast the reasoning into more general formulae. Those who are not entirely happy with algebraic manipulations are thus able to at least understand the gist of the argument.
A worthwhile book for those who like mathematical brainteasers to compensate for less demanding work schedules. A good book in the hands of the gifted youth who wishes to develop his abilities. A good source of problems for those who prepare for mathematical competitions or (perhaps) tests on undergraduate level. A useful source for entertaining problems suitable for the card table. Pure entertainment for those who think mathematics is indeed entertaining.