Overview
Bayes rule allows one to calculate the conditional probability {% \mathbb{P}(B_j|A) %} when the reverse conditional probabilities {% \mathbb{P}(A|B_j) %} and the individual probabilities {% \mathbb{P}(B_j) %} are known.
Bayes Rule
{% \mathbb{P}(B_j|A) = \frac{\mathbb{P} (A|B_j) \mathbb{P}(B_j)}{\sum_{i=1}^n \mathbb{P}(A|B_i) \mathbb{P}(B_i)} %}