P(A∪B) = P(A) + P(B) − P(A∩B). The intersection term is what trips people up — independent events multiply, dependent events need conditional probability.

Binomial: probability of exactly k successes in n trials. Use for fixed-trial yes/no scenarios like coin flips or product defects.

Poisson: rate-based counts (calls per hour, typos per page). Z-score tail probabilities convert any normal distribution to standard form for table lookups.