1.9 Bayes’ Theorem

Now that we understand the various probabilities, we can use this knowledge to understand and apply Bayes' theorem (named after the Reverend Thomas Bayes). This theorem has a central place in the probabilistic theory and gives us a completely new perspective to think about probability.

Bayes’ theorem provides a structured way to convert a conditional probability from one direction, say (|), to the other direction, (|). When dealing with decision-making or scientific inference, it allows us to update our beliefs in the light of new evidence. Mathematically, Bayes’ theorem can be denoted as:

         , provided that () > 0