Chances Are . . .: Adventures in Probability

This is a truly phenomenal book! As a mathematician and a mathematics educator I have certainly studied and taught the mathematics of probability theory and statistics. I have always worked to convey to my students the story of the subject (mathematical story that is) and the intellectual context of the work, as well as convey a sense of the overall structure of its historical development. But I am a tad embarrassed to admit that I did not truly appreciate the *human context* of this subject until I read CHANCES ARE .... Ellen Kaplan and Michael Kaplan have pieced together, clearly after a phenomenal amount of archival research, the picture of man's struggle to harness chaos and randomness in his life. The story they tell is compelling and richly human. Divided into 11 chapters, each section of text deals with the story of one particular aspect of the unpredictable - understanding the spread of disease and the effectiveness of vaccines, for instance, the role of the uncertainty in the courtroom, the effects of the unpredictable in political interactions and warfare, all connected to the innate human desire to master the unknown. Ellen and Michael not only explore factual details related to describing, accepting, and, in some cases, conquering uncertainty, but also discuss and reveal the psychological impact randomness induces at every stage of its contemplation. Reading their work becomes a personal experience: we see that the struggles encountered by a society are the personal struggles we each experience. This book is revealing on a multitude of levels. Written with humor and eloquence, the book is a delight to read. Although mathematical formulae are kept to a minimum, mathematical richness of ideas is not denied. As an educator, I hope this book will become required reading for all students of probability and statistics. But this, of course, is not the only audience of readers. CHANCES ARE ... is an important book, absolutely relevant and accessible to all who are human. It is fundamentally a book about us.

This is an especially informative and entertaining book. It makes a great read. In fact it is worth putting by for re-reading. There is plenty to mull over. It draws humour from the gap between what is possible and what actually happens. Statistics and probability shimmer here, like Jeeves, ever ready to be consulted. What are the chances of my ship coming home without being sunk in a storm? Should I hedge my bets? As the authors see it, if uncertainty is our lot, then probability is the science of getting on with life. They reveal just what a human interest story and an absorbing study it is. And also deep: some of the results go well beyond intuition, and some are actually counter-intuitive and likely to make the reader very curious to hear the theory behind them. Basic principles are explained over the course of the book. The reader with leisure can easily test some things at first hand. We are shown why calculation is necessary, even if it forces our minds first to acknowledge a gap that we are often more keen to leap. Even if the necessity for numbers is something we regret, I think most of us will find it yielding easily enough to the authors' pleasant and humorous approach. The pace is fast: I felt I was listening to rapid double fire from the authors, mother and son, now playing a couple of comedians, now professors. We glimpse Aristotle's ideas of science and of ethics, Descartes' knowledge revolution, Pascal's approach to salvation, the spirit of Laplace, as the authors take us through the historical development of the notion of Chance. In medieval times apparently this notion just could not be taken for granted and much was ascribed to God's will. It took a while to establish probability as a ratio between one possibility and many. Imagine a range of possibilities where each is as likely as any other but just one will happen. If an event we are interested in can be represented as one such possibility or as the selection of several as an "each way" bet, then the ratio between the selection total and the grand total is the probability of the event. Almost axiomatic, you'd think? Yes, but there may be trouble ahead! In the meantime, we find this approach allows for interesting tricks and techniques and solutions to betting problems and more besides. Here also to admire are Pascal's triangle and the bell curve, de Moivre's brilliant standard deviation idea and, if we toss a coin, say, 3600 times, we have a way of calculating how likely we are to arrive within a given range of deviation from perfectly even totals. As for that trouble ahead, the authors draw attention to the problem that cards and coins can be biased and can be the stuff of cheating, and maybe perfect dice are impossible to make anyway. More generally, how could we ever know that we had truly analysed a practical problem exhaustively into exclusive, independent, and equal possibilities, or that an event in which we are interested could really be defined as a selection of

This is a very special book. Michael and Ellen Kaplan put forth an intriguing thesis. We are taught deductive reasoning in geometry and logic classes, inductive reasoning in science. This book is about the great valley in between where we spend most of our lives: probability. They throw us some fun problems at the start to show that many of us (e.g. me) may not grasp probability intuitively. The "Blue Cab/Green Cab Problem" is an eye opener. If 85 percent of the cabs in a city are green, 15 percent blue, and a witness with 80 percent accuracy spots a blue cab, is it likely to actually be blue or green? The answer is surprising. People focus on the 80 percent accuracy, but the key is the 15 percent of blue cabs. This is more than a fun math problem. It can help you judge medical tests. A less-than-perfect diagnostic test of a rare condition is likely to be misleading. (Don't depend on your doctor; the Kaplans show that MDs are not good at probabilities.) There is a wonderful chapter on gambling and some new insights into Pascal's Wager. Pascal says to bet on the existence of God; the Kaplans, after doing the math, are not so sure. Again, this is more than just an academic exercise. A band of Evangelical Christians are currently going around our community using Pascal's Wager as an argument for converting young people to their fundamentalist Christianity. The authors also address the Monty Hall problem: whether a contestant on "Let's Make a Deal" should switch doors when Monty reveals what's behind one of them. Everybody knows by now, if they've read about the problem in USA Today or the NY Times, that one always swtiches. But the Kaplans are the first to explain the theoretical underpinnings of the problem, comparing it to the Principle of Restricted Choice in bridge. There's more. Philosopher David Hume said that the fact the sun has risen every morning is no proof that it will rise tomorrow. But the Kaplans show that Bayesian probability offers math that is not proof per se, but evidence of probability. My psychotherapist suggested I use Bayesian probability to help deal with my great variety of unrealistic anxieties. I am terrified, for example, of having to go to the bathroom on a long bike ride with no restroom nearby. Actually calculating the probability of this happening, using past experience, has relieved this nervousness. The best thing about the book, though, is its tone. Most math-book authors are making one point: they are smart and everybody else is dumb. The Kaplans are not arrogant, and explain why it's natural that we make the mistakes we do. They poke fun at the "geniuses" at the RAND Corporation who got annoyed when people refused to act like RAND mathematical diagrams predicted they would act. The RAND folks tried to convince two presidents to make a preemptive nuclear strike at the Soviet Union, but thankfully dumber but more experienced men prevailed (Truman and Eisenhower). An excellent book. There is a 100 percent chance

I loved this book! It's a quick read and received high praise by the New York Times and the New Yorker, so my humble comments only echo those. This book weaves a rare combination of entertaining stories with precise lessons of how risk and randomness affect our daily lives. One can tell the authors' depth of experience and love of teaching the interplay of mathematics, philosophy and the human condition. The mother and son authors chose a wide variety of historical vignettes and modern life dilemmas, making the discussions very accessible and entertaining. I enjoyed Steven Levitt's Freakonomics for its mix of illuminating stories, but I felt like this book explored a richer set of classic historical examples and many more lessons on risk that I can apply to my real-life decisions.