Probability Calculator

About the Probability Calculator

Probability quantifies the likelihood of events occurring, expressed as a value between 0 (impossible) and 1 (certain), or equivalently as a percentage. Our probability calculator handles single event probability, complementary probability, combined independent event probability, and conditional probability — the four core calculations in introductory probability theory.

How It Works

Single event: P(A) = favourable outcomes / total outcomes. Complement: P(A') = 1 − P(A). Combined independent events: P(A and B) = P(A) × P(B). Either event: P(A or B) = P(A) + P(B) − P(A and B). Conditional probability: P(A|B) = P(A and B) / P(B). Example: Drawing two aces from a deck without replacement: P(first ace) = 4/52, P(second ace) = 3/51, P(both aces) = (4/52) × (3/51) = 0.45%.

Tips & Best Practices

• ✓Mutually exclusive events cannot occur simultaneously — P(A or B) = P(A) + P(B) for mutually exclusive events.
• ✓Independent events do not affect each other — coin flips are independent; cards drawn without replacement are not.
• ✓The birthday problem: in a room of 23 people, there is a 50% chance two share a birthday (counterintuitive).
• ✓Expected value = Σ(outcome × probability) — fundamental concept for games, insurance, and investing.
• ✓p-value in statistics is a probability — the chance of observing results as extreme as yours under the null hypothesis.

Who Uses This Calculator

Statistics students, data scientists calculating model confidence, insurance actuaries pricing risk, gamblers evaluating odds, and quality control engineers calculating defect probabilities all use fundamental probability calculations.