Bayes' theorem reverses the direction of conditional probability. Given partition B_1, B_2, ..., B_n of the sample space:

P(B_i|A) = P(A|B_i) * P(B_i) / [sum over j: P(A|B_j) * P(B_j)]

The denominator is the Total Probability: P(A) = sum P(A|B_j) * P(B_j).

Step-by-step approach (BAIT):

1. Branches: Identify the partitioning events (e.g., which box, which machine)
2. Assign priors: Write P(B_i) for each branch
3. Input likelihoods: Write P(A|B_i) — probability of observed event given each branch
4. Total and compute: Calculate denominator then apply formula

Common JEE pattern: "Given the item is defective, what is the probability it came from machine A?" This is a classic reverse conditional — use Bayes'.