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Independent Events Probability Calculator — result sheet
Find the probabilities of both, either, exactly one, or neither of two independent events.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: With probabilities a and b as fractions: both = ab; at least one = a+b-ab; exactly one = a(1-b)+b(1-a); neither = (1-a)(1-b).
Independence means observing one event does not change the probability of the other. Under that assumption, their joint probability is the product. The union subtracts the overlap once, and exactly one excludes the both-events outcome. Inputs and outputs are displayed in percentage points.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Probability of event A — %; minimum 0; maximum 100
- Probability of event B — %; minimum 0; maximum 100
Worked example
| Input | Value |
|---|---|
| Probability of event A | 50 |
| Probability of event B | 20 |
10%
Assumptions and limits
- Events A and B must be independent; these formulas do not infer independence from the supplied percentages.
- Independent and mutually exclusive are different concepts.
- Each probability is entered from 0 to 100, so enter 50 for a 50% chance, not 0.5.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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