Given the reviews at Amazon, this warning is likely unnecessary, however, if you are hoping for a detailed survey of the mathematics of applications of the ideas initially explored by Bayes, Price, LaPlace and developed extensively (wittingly or otherwise) throughout the 20th century, this is not the book you are looking for.
The author's writing style is pleasant, concise, easy to read and has good forward momentum, without being as important a component of the story as, say, Bill James or Mary Roach or Jon Ronson or Buzzy Jackson are in their books. (Regular readers of my reviews know that my favorite non-fiction genre is where a person goes, hmmm, how does _this_ work and then proceeds to read up on it and then interview people and perhaps do little experiments themselves and then the book itself is about the entire process, not just the-answer-to-the-original-question which by this point may or may not even be interesting compared to what turned up along the way.) As the subtitle indicates, the author has a thesis: Bayes-Price-LaPlace is [dramatic music here] Amazingly Useful.
The first sections of the book are really excellent: she describes the world in which Bayes had his idea, what he didn't do with it, how Price came to dig it back out again, and how that largely sunk as well, and then how LaPlace really ran with it a while later. Easily the best thing about this book is that it firmly connects mathematics (and not just Bayes-Price-Laplace) to non-mathematical activities that people need help with.
The section on WW2 and Enigma felt very different from versions of this story that I have read in the past. That doesn't mean I think they were wrong, just that McGrayne is drawing attention to strands in events that had not made it into things I read before, and she includes some ideas as to _why_ they were left out. The postwar bits about feuding statisticians was not as entertaining to read about as it seems like it should have been (I'm usually amused by scandalous backbiting but in this case I was a little bored and at times annoyed, possibly because some of the participants sounded way too much like people I've run across in computer science). The last section (which included stuff about Clippy that I just did not actually believe) was the weakest -- a very high-level summary of people using Bayesian ideas for everything.
It works well as history for the non-mathematical. It'll be frustrating for anyone who _really_ understands the mathematics. And a generalist who would like yet-another-take on science history should have a blast. It's a great book and I suspect it will reward rereading.