Calculator Inputs
Formula used
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
P(A ∩ B) = P(A | B) × P(B)
P(A ∩ B) = P(B | A) × P(A)
P(A | B) = P(A ∩ B) / P(B)
P(B | A) = P(A ∩ B) / P(A)
Independent events: P(A ∩ B) = P(A) × P(B)
Mutually exclusive events: P(A ∩ B) = 0
How to use this calculator
- Enter practical event names, such as pump failure and sensor trip.
- Select whether inputs are percentages or decimal probabilities.
- Type the two base probabilities for the events.
- Choose the known setup: intersection, union, conditional value, independence, or exclusivity.
- Enter the extra known value when the setup requires it.
- Add a sample size to convert probabilities into expected counts.
- Press calculate to show results above the form.
- Review the chart, then export the output as CSV or PDF.
Example data table
| Scenario | P(A) | P(B) | Known input | Resulting P(A ∪ B) |
|---|---|---|---|---|
| Cooling fan fault and sensor alarm | 0.18 | 0.12 | P(A ∩ B) = 0.05 | 0.25 |
| Valve leakage and pressure drop | 0.22 | 0.17 | P(A ∪ B) = 0.31 | 0.31 |
| Motor overload and breaker trip | 0.14 | 0.20 | P(A | B) = 0.35 | 0.27 |
| Independent vibration and heat alerts | 0.09 | 0.16 | Independent | 0.2356 |
Frequently asked questions
1. What does this calculator solve?
It evaluates two-event probability relationships. You can compute union, intersection, conditionals, complements, exclusive outcomes, and expected counts for engineering risk, reliability, and alarm analysis.
2. When should I choose the independent option?
Choose independence when one event does not change the likelihood of the other. In that case, the shared probability equals the product of the two individual probabilities.
3. What does mutually exclusive mean here?
Mutually exclusive events cannot happen together. The calculator sets the intersection to zero, then adds the two individual probabilities to find the union.
4. Can I enter percentages instead of decimals?
Yes. Select percent mode to use values like 35 and 12. Select decimal mode to use values like 0.35 and 0.12 instead.
5. Why does the calculator show an impossible input warning?
Your entries may violate probability rules. Common causes include an intersection larger than either event probability, or a union smaller than one event probability.
6. How are expected counts useful?
Expected counts convert probabilities into approximate event numbers for a chosen sample size. That helps compare inspection batches, operating hours, or test cycles.
7. What is the independence gap?
It is the absolute difference between the actual intersection and P(A)×P(B). A zero or very tiny gap suggests the data is consistent with independence.
8. Is this only for engineering projects?
No. The layout is engineering-focused, but the math also works for finance, quality control, operations, medicine, education, and any two-event probability problem.