Rosenthal, Jeffrey S. Struck by lightning: The curious world of probabilities. Toronto: HarperCollins, 2005. 264pp.
This is a good, fun, breezy, quick-read popular math book. And that's a good thing, as there probably aren't too many of that type out there. This is certainly at a level that any average, intelligent person over the age of 15 could easily understand; and certainly, any precocious girl or boy over 10 or 11 will get a real kick out of it -- it's something that will certainly fire their mathematical imaginations.
This is a book about statistics and how the use and abuse of statistical analysis is prevalent in our daily lives, in the everyday decisions we make and the information we consume in the media. It aims to cut through the crap and give us, the common folk, the tools to see when we're being conned, to make better decisions about risks we could face and to just understand all those news reports about medical and other scientific studies. Rosenthal uses a clear and light-hearted presentation, heavy on humour and light on equations, with lots of examples to make each topic come through as clearly as possible. He uses little humourous anecdotal asides quite often to make the discussions more concrete. On the other hand, he also doesn't over-present. The sections are mostly short and sweet, making their points and getting on with it. Sometimes it makes things seem a bit scattershot; for example he covers probabilities in a bunch of different card games in only a few pages.
The opening two chapters are an introduction to probabilities in our everyday life and how we should approach cases where chance and coincidence come up. Chapters 3 and 4 are among the most interesting as they deal with how casinos use probability to make sure they always win in the long run. Chapter 5 on understanding crime statistics, 6 on decision making and evaluating probabilities, 7 on scientific studies and 8 on events with very low probabilities.
The second half of the books covers a lot of the same kind of ground: chapter 10 on opinion polls, 11 on margins of error, 12 on uncertainty, 13 on biology, 14 on the famous Monty Hall problem, 15 on using statistical analysis to combat spam emails and chapter 16 a nice summary of the main themes, bringing in a bit of quantum theory to talk about the causes of randomness. The final chapter is a fun little multiple choice quiz to make sure we understood what came before.
A couple of cool things he covers? For example, he talks about the probabilities of aliens on page 123, making decisions using utility functions as it applies to dating in chapter 6. As I mentioned, he uses humourous asides to explain a lot of points. here's a good one on utility functions (ie. decision making) on page 93:
The Naughty Nephew
Your adorable little nephew is over for a visit, and he is playing with his favourite ball. You told him to be careful, but he is being nothing of the sort. He has already broken a glass, and after you yelled at him he knocked down a picture. How can he be so unreasonable? Obviously, from your point of view, damaging a glass and a picture is far more serious than a bit of fun with a ball.
You then consider your nephew's utility function. He loves playing with the ball, the wilder the better, and might rate the activity at +20. On the other hand, he only feels a little bit bad when he breaks things and gets yelled at, perhpas a -10. So, from his point of view, his actions are completely reasonable.
Part of you feels you should teach your nephew to be responsible by punishing him or taking away his ball. Then again, perhaps his utility function isn't so crazy after all. As a compromise, you carefully remove all the remaining breakable objects from the room, and allow your nephew to continue playing. You belongings are safe, your nephew can play wildly with his ball, both of you utility functions are respected, and you are both happy.
For me, the greatest service this book served was to finally explain the famous Monty Hall problem. You know, like on Let's Make a Deal or Deal or No Deal? You have to choose between first three doors for the prize, then after you choose one the host eliminates one of the remaining and makes you choose again between the last two? I'd read a bunch of explanations of the solution in a bunch of other places. They always made perfect sense while I was reading them. But as soon as I finished, my mind would go blank. Rosenthal actually has an explanation that seems to be sticking.
My libraristic recommendations? Any academic library that carries any popular science would do well to get this book, as would really any public library. High school libraries for sure, and even middle school libraries who get books for the really bright kids.