If you've read Science 2.0 for any length of time, you've seen Bayes' Theorem - mostly in sports.  We use it to predict who will win the baseball playoffs, for example.  

Bayes’s theorem, named after 18th-century Presbyterian minister Thomas Bayes, has become an invaluable tool for scientists. 

At its core, Bayes’s theorem depends upon an ingenious turnabout: If you want to assess the strength of your hypothesis given the evidence, you must also assess the strength of the evidence given your hypothesis. In the face of uncertainty, a Bayesian asks three questions: How confident am I in the truth of my initial belief? On the assumption that my original belief is true, how confident am I that the new evidence is accurate? And whether or not my original belief is true, how confident am I that the new evidence is accurate?

New York Times writer John Allen Paulos tackles how Bayes theorem cracked the Enigma Code, hunted down Russian submarines, outlined in the book THE THEORY THAT WOULD NOT DIE by Sharon Bertsch McGrayne,