Conditional probability and multiplication theorem: P(A|B) = P(A∩B)/P(B) (probability of A given B occurred). Multiplication: P(A∩B) = P(A) × P(B|A). For independent: P(A∩B) = P(A) × P(B). Bayes' theorem: P(A|B) = P(B|A)×P(A) / P(B). Example: Disease test. P(disease) = 0.01, P(positive|disease) = 0.95, P(positive|no disease) = 0.05. P(positive) = 0.95×0.01 + 0.05×0.99 = 0.059. P(disease|positive) = (0.95×0.01)/0.059 ≈ 0.161. Solving: Identify conditional relationships. Build probability tree. Apply Bayes for posterior probability. Exam tip: Understand prior, likelihood, and posterior. Practice: Medical test, reliability problems.