The main challenge in writing a mathematics book for a popular audience is to convey the subject to a wide readership while at the same time maintaining reasonable standards of mathematical rigor. In Probabilities, which includes several references to mathematically-related scenes in episodes of Seinfeld, the challenge is met successfully.
Some of the Seinfeld references are a reach — a mention of a toy dinosaur in a cereal box in “The Doll” went no further, mathematically, on TV — but they tend to lead into worthy explanations of probability. In this case, the coupon problem is examined in great detail, accessible to the reader with limited knowledge of probability (or of Seinfeld).
Olofsson’s coverage of the Monty Hall problem is unusual in that it includes a plausible explanation for the mathematical community’s resistance to Marillyn vos Savant’s original answer. In fact, vos Savant has recently caught up to him, in a recent column in Parade magazine that addresses the related problem where Hall opens a random door rather than one known not to conceal a goat. Whether or not this is what people were collectively thinking in 1991, it is good to see this alternative presented.
Before long, we see solid mathematics appearing, complete with summation signs and some careful theoretical considerations. There is enough serious mathematics here to satisfy most purists, but it’s combined with an engaging writing style and clever examples that make for a fine addition to the popular literature on probability.
Mark Bollman (firstname.lastname@example.org) is an assistant professor of mathematics at Albion College in Michigan. His mathematical interests include number theory, probability, and geometry. His claim to be the only Project NExT fellow (Forest dot, 2002) who has taught both English composition and organic chemistry to college students has not, to his knowledge, been successfully contradicted.