Probability Calculator
Calculate the probability of a single event, its complement, the union or intersection of two events, or a conditional probability — with the exact formula and steps shown.
0–1
PROBABILITY RANGE
5
CALCULATION MODES
Live
INSTANT RESULTS
Single Event
Enter how many outcomes count as a “success” out of the total possible outcomes.
Result
0.166667
16.67%
- Decimal
- 0.166667
- Percentage
- 16.67%
- Odds
- 167:833
Formula & Steps
P(A) = Favorable Outcomes / Total OutcomesP(A) = 1 / 6
P(A) = 0.166667
Probability Scale
Understanding Probability
Probability measures how likely an event is to happen, expressed as a number from 0 (impossible) to 1 (certain). For equally likely outcomes, it’s simply the count of favorable outcomes divided by the total number of possible outcomes — rolling a specific number on a fair die, for instance, has a favorable count of 1 out of 6 total faces, giving P = 1/6 ≈ 0.167. Once you can find that single-event probability, the rules below let you combine events to answer richer questions.
The Five Core Rules
Complement: P(not A) = 1 − P(A) — the chance A does NOT happenUnion: P(A∪B) = P(A) + P(B) − P(A∩B) — the chance A OR B (or both) happensIntersection: P(A∩B) = P(A) × P(B|A) — the chance A AND B both happenConditional: P(A|B) = P(A∩B) / P(B) — the chance of A given that B already occurredIndependence: P(A∩B) = P(A) × P(B) — true only when knowing B tells you nothing about AIndependent vs. mutually exclusive: these two ideas are easy to mix up but describe opposite relationships. Mutually exclusive events (like rolling a 4 or a 5 on the same die) can never happen together, so P(A∩B) = 0 and the union rule simplifies to addition. Independent events (like two separate coin flips) can absolutely happen together — one just doesn’t change the odds of the other, so the intersection rule simplifies to multiplication. Choosing the wrong assumption is one of the most common probability mistakes, so this calculator asks you directly which one applies before combining P(A) and P(B).
🎲
Single Event
Favorable outcomes divided by total outcomes. The building block every other rule relies on.
🔄
Complement
Everything that isn't A. Often the easiest path to "at least one" problems — find P(none), then subtract from 1.
∪
Union (OR)
Subtract the overlap once so events counted in both A and B aren't double-counted.
∩
Intersection (AND)
Multiply straight across if independent; otherwise multiply by the conditional probability instead.
— FAQ