Bayes theorem relates conditional probabilities: P(A|B) = [P(B|A) × P(A)] / P(B). Denominator P(B) = Σ P(B|A_i) × P(A_i) for all possibilities. Key concepts: updates initial probabilities with new evidence. Common traps: confusing which probability is in numerator, missing denominator calculation. Exam tips: organize events clearly, calculate all components. Time-saving: use systematic table approach. Prior probability: P(A) before evidence. Posterior probability: P(A|B) after observing B. Likelihood: P(B|A). Applications: medical diagnosis (disease given test result), spam detection, quality inspection. Real example: if disease is rare (low prior), false positives common (confusion with likelihood). Understanding Bayes essential for decision-making. Practice with medical and business scenarios.