Stephanie Glen gives us the basics of Bayes’ Theorem in a picture:
Bayes’ Theorem is a way to calculate conditional probability. The formula is very simple to calculate, but it can be challenging to fit the right pieces into the puzzle. The first challenge comes from defining your event (A) and test (B); The second challenge is rephrasing your question so that you can work backwards: turning P(A|B) into P(B|A). The following image shows a basic example involving website traffic. For more simple examples, see: Bayes Theorem Problems.
Click through for the image and related links.