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

This is recreational math at its finest. All problems are approachable with just elementary probability theory and high school mathematics with the occasional appearance of first-semester calculus. However, each problem is thought-provoking and lead to interesting generalizations, if the reader is so inclined. I have seen maybe six or seven of the problems in previous contexts (I'm not particularly well-read in this area of math), but the solutions provided by the author still gave me something the think about. The rest of the problems were brand new for me and were good to think about on a lazy Sunday afternoon. Good if you're a math nerd, or you're trying to get a new generation of young'uns hooked. A bit on the short side -- it leaves you wanting more.

I was compelled to write a review as I found some of the lower-ranked reviews downright condescending. Some of the problems in the book are decidedly simple but with twists that may not be obvious at the outset. In hindsight, the solutions to these make them simple to understand and replicate. But several other problems discussed are difficult enough to be posed on Ph.D qualifiers at class 1 institutions. That is the appeal of the book. Its a great mix. I read some of the tough problems regularly to deepen my understanding of logically working through a solution. I have used Buffon's needle (before I read this book, but it is discussed therein) on my 10 yr old's school project and used the "breaking a stick" problem to illustrate Monte Carlo simulation in class. Granted that some knowledge of basic probability/mathematical statistics would be required to appreciate the solutions but even without such a background the problems themselves are fairly interesting. For example, I have posed the "tennis" problem to my 10 year old and have worked through the logic with him, which he understood sans any math. In summary, this is $7 and change more than well spent.

picked this up to supplement my probability class and it is exactly what it sounds like, fifty problems that will make your brain hurt in a good way. some of them are pretty straightforward and others are genuinely tough so there is something for every level. the solutions are explained well enough that you can actually learn from them rather than just copying the answer.

This is an excellent book. The puzzles are interesting and the solutions not always very simple. So, it is a lot of fun solving the problems. The selection of problems is great and very explanatory and detailed solutions are provided at the end.

The problems in this book are a master class in the variety of and intellectual robustness within even simply stated questions. Some solutions border on the whimsical. Many have multiple approaches to their solution. The solutions are complete, but not overly explained. Many solutions leave some small and other thoughtful "leaps" for the full details to be appreciated. At first this can be annoying, but once you "step it up", you can't help getting productively engaged.

This is a fun book, with bite-size probability problems and an answer key provided in the back. If you enjoy probability and statistics, you’ll have fun with this book. I like to read one a day and think it through on my morning drive. Some old classics and some new problems included in here; it would make a nice little gift too.

I did one problem each morning. Really happy with most solutions, though some could have shown more steps. The author covers famous problems like Buffon's needle and Molina's urn, and also shows how simple probability problems can lead to several of the most common probability distributions.

I enjoy solving probability puzzles. I considered myself to be pretty good- I could solve any problem that the GRE practice exams could throw my way. Until I opened this book. This book takes off where I ended up. The first problem is a variation on the "reach into a bag" probability problem. (Q: You reach into a drawer with red socks and black socks, and the probability of drawing 2 red socks is P=0.5. What is the minimum number of both colored socks?) You won't find the typical probability problems that can be quickly solved with basic combinatorial analysis or the Bernoulli Coefficient. You'll find variations and completely new worlds of probability. The explanations are thorough but succinct, and will arm you with a new skill set for solving such problems. There's no other book like it on Amazon, and for $7... Comparable to Huff's "How to Lie with Statistics" in its originality and straight-forwardness.

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I bought this because I used to be not so good at probabilities. The book is very entertaining and it seems to cover most simple probability ideas. I was surprised how people with BAC+6 specialized in probabilities (even from the "famous" DEA El Karoui) could not find the answer of some of those elementary probability problems.

Non è un caso che i problemi proposti siano stati ripresi da altri autori nel corso degli anni (il libro è del 1965), essi costituiscono uno stimolo prezioso. Dubbi su una o due soluzioni proposte.

Lo compré porque me encantan las matemáticas. Es una colección de problemas con solución sobre temas realmente complicados de probabilidad. Si te gustan los retos numéricos, éste es tu libro! ***** SI ESTA OPINIÓN TE HA PARECIDO ÚTIL, POR FAVOR, DALE A «SÍ» *****

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.