The plot of Agatha Christie’s “By the Pricking of My Thumbs” reaches a point early on where Mrs. Beresford, known to her friends as Tuppence, is just about convinced that her instincts and suspicions are mistaken. She is about to move on with her life when she receives a telephone call from Dr. Murray, the attending physician at the retirement home where her husband’s aunt had recently died.

At lunch, he told her, in strictest confidence, about three deaths at the rest home that made him uneasy. He used these words to express his doubts: “They were perfectly probable, they were not unexpected, but I will go as far as saying that they were unlikely.”

Mystery novels and detective movies owe a lot to characters like Dr. Murray. Their questioning minds have formed a kind of instinct for things that aren’t quite right; things that invite questions to a mind that is open enough to permit their entry.

There are people like that in real life, too, and we owe a lot to them. They are the detectives who keep working on a case even though there is a suspect in custody. And they are the scientists who ask precisely the right questions — even when the conventional wisdom has everyone else satisfied.

Persi Diaconis and Brian Skyrms are people like that. They are both professors at Stanford University — Diaconis in math and statistics; Skyrms in logic and philosophy — and their new book contains both some questions and some answers.

The book is entitled “Ten Great Ideas About Chance” (Princeton University Press), and it contains not only those ideas but also the questions that prompted their discovery. In doing so, readers get a sense of the history of how today’s knowledge of probability came to be what it is. It also provides us with a sense of what questioning minds are capable of, and how they have become a major influence on our lives.

Probability theory isn’t just for casino games or for sports gamblers working the point spreads. It plays an important role in the medicines that cure people, for example. And it plays a role in sports, too, even though it is often misunderstood.

“Ten Great Ideas About Chance” recounts how Thomas Bayes, who died in 1761, provided the breakthrough that broke the German “Enigma” naval code that contained the disposition of the U-boats and threatened to choke off Britain’s ocean lifelines. It was Bayes’ theorem that opened the “unbreakable” encryption system and allowed the British to read the messages.

In some respects, the origins of Bayes’ work in probability are as important as the work itself. Essentially, he was dissatisfied with existing theory of chance, and began asking questions about the underlying math, reasoning and logic.

Those questions. and more like them, are still valid today, despite Bayes’ work in advancing our knowledge. Statisticians, for example, have been railing for years about the poor quality of statistical inference used in evaluating the effectiveness of new drugs. The cause is an overdependence on a measure of results, called a “p-value,” which calculates a comparison of results with the probability that they could have been caused by random chance.

In a section entitled “Why Most Published Research Findings Are False” — which is the title of a well-known research paper on the subject written by John P.A. Ionnidis — authors Diaconis and Skyrms say many medical research results cannot be replicated by independent researchers, even with the help of the original researchers. This explains why we have so many new drugs that seem effective in trials but fail to deliver results in actual use. The same flawed inference process also explains why political polls are so often wrong, despite their calculated “margin of error.”

“Ten Great Ideas About Chance” isn’t just about 18th century philosophical arguments, World War II events or tests of expensive, hard-to-pronounce drugs. The books ideas are as down to earth and as current as your busted bracket for NCAA Men’s Basketball.

Sports have been infested with “analytics” that are supposed to help make better decisions. Basketball coaches, for example, in choosing a last-minute play, might consult the stats on making three-pointers vs. two-pointers and foul shots. Most successful coaches are too competent to rely on averages for a decision, though, since they know that the average from the past doesn’t really tell you anything useful about the probability of success on the next play.

Most of us aren’t coaches but we sure could use a refresher course in the rewards and limitations of statistical inference. And we could all use a better understanding of why the statistical underpinnings of medicine and politics so often produce disappointing results. The odds are that we’ll find it useful.

James McCusker is a Bothell economist, educator and consultant.