Probability Calculator

Probability Rules

P(A AND B) — Independent Events

Multiply probabilities: P(A∩B) = P(A) × P(B). Rolling a 6 twice: 1/6 × 1/6 = 1/36. Works ONLY when events are independent — the outcome of one doesn't affect the other.

P(A OR B) — Addition Rule

P(A∪B) = P(A) + P(B) − P(A∩B). Subtract the intersection to avoid double-counting. For mutually exclusive events (can't both happen): P(A∪B) = P(A) + P(B).

Conditional Probability

P(A|B) = P(A∩B) / P(B). The probability of A given that B has already occurred. A positive COVID test given you're in a low-prevalence population has a much lower probability of being a true positive than it first appears — the base rate matters enormously.