Probability Calculator
Adjust the inputs below. Results update as you type.
How it works
P(A and B) = P(A) × P(B) if independent. P(A or B) = P(A) + P(B) − P(A and B). Conditional: P(A|B) = P(A and B) / P(B). Bayes: P(A|B) = P(B|A) × P(A) / P(B). Common mistake: independence does not equal mutual exclusivity—mutually exclusive events can't both occur, independent events don't affect each other. Complement rule: P(not A) = 1 − P(A).
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
Probability = favorable outcomes ÷ total outcomes. Independent events multiply: P(A and B) = P(A)·P(B). Mutually exclusive events add: P(A or B) = P(A) + P(B).
Worked example
Rolling two dice, the chance of two sixes is (1/6) × (1/6) = 1/36 ≈ 2.8%.
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Quality-reviewed for publication with formula checks and explanatory copy updates.
Site-wide corrections also appear on the corrections log.
Build math and logic skills with guided lessons
Educational platform recommendation.
Frequently asked questions
What is the difference between 'and' and 'or'?+
For independent events, 'and' multiplies probabilities; 'or' (for mutually exclusive events) adds them, then subtracts any overlap.
What does probability 0 or 1 mean?+
0 means impossible, 1 means certain. Everything else falls between, expressed as a fraction, decimal, or percentage.
What are independent events?+
Events where one outcome does not affect the other, like separate coin flips. Their joint probability is the product of the individual ones.
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.