Probability Calculator
Calculate P(A and B), P(A or B), P(not A), conditional probability and more for independent, exclusive or joint events.
Your inputs
Results
P(A and B)
0.2
- P(A or B)
- 0.7
- P(not A)
- 0.5
- P(A given B)
- 0.5
- P(neither)
- 0.3
- P(exactly one)
- 0.5
✓Exact calculation — rounded only for display
What this calculator does
Combine two event probabilities correctly depending on how the events relate.
Formula and method
Independent: P(A∩B) = P(A)P(B); Exclusive: P(A∩B) = 0; P(A∪B) = P(A) + P(B) − P(A∩B); P(A|B) = P(A∩B) ÷ P(B)
Worked example
Calculated by this tool with its default inputs:
Inputs
- P(A): 0.5
- P(B): 0.4
- Relationship between A and B: Independent
Results
- P(A and B): 0.2
- P(A or B): 0.7
- P(not A): 0.5
- P(A given B): 0.5
- P(neither): 0.3
- P(exactly one): 0.5
How to read the results
Inconsistent inputs (such as P(A∩B) larger than P(A)) are rejected.
Assumptions and limitations
- Probabilities are entered as decimals between 0 and 1.
Questions
Independent vs mutually exclusive?
Independent events do not affect each other; mutually exclusive events cannot happen together.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 4 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy