How it works
Adding the probabilities counts the overlap twice, so subtract it once. For P(A) = 0.6, P(B) = 0.5 and overlap 0.2, the union is 0.9 and the probability of neither event is 0.1. The overlap cannot exceed either event, and must be at least max(0, P(A) + P(B) − 1).
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| P(A) | 0.6 | Enter a numeric value. Use a non-negative value. Allowed range: 0–1. |
| P(B) | 0.5 | Enter a numeric value. Use a non-negative value. Allowed range: 0–1. |
| P(A and B) | 0.2 | Enter a numeric value. Use a non-negative value. Allowed range: 0–1. |
Worked example
Show example inputs and results
This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.
- P(A)
- 0.6
- P(B)
- 0.5
- P(A and B)
- 0.2
Complete example results
- Union probability P(A or B)
- 0.9
- Probability of neither event
- 0.1
Reading the result
Check the probability scale, sample size and assumptions stated by the method. A decimal probability of 0.5 represents 50%. Mean and spread inputs must describe the same dataset; the calculation does not validate those estimates.
Questions and answers
Can I use the example values for my own calculation?
The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.
Must I assume the events are independent?
No. Supply their actual joint probability. Only under independence does the overlap equal P(A)P(B); mutually exclusive events instead have zero overlap.
Why are some results rounded?
Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.
Are my inputs sent to a server?
The calculator processes inputs in your browser. Its code does not send your values to a server.
Method sources: openstax.org