Description
Calculate neither-event and at-least-one probabilities under independence.
Probability calculations distinguish event mass, density likelihood, support membership and interval inclusion. Zero likelihood is not always proof of impossibility, and a known zero-probability category differs from an absent label. Independence, disjointness and supplied CDF values are assumptions or records, rather than properties established by local arithmetic.
Calculate neither-event and at-least-one probabilities under independence.
When to use this tool
Use Independent Complement Product Two Events when you already have firstProbability, secondProbability and need to calculate neither-event and at-least-one probabilities under independence.
How to use the tool and how it works
- Enter firstProbability, secondProbability. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read neitherProbability, atLeastOneProbability. Use the output convention below.
Require both probabilities in [0,1]; neither=(1-p)*(1-q), atLeastOne=1-neither.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstProbability | First Probability | Required. Finite number; minimum 0; maximum 1. |
| secondProbability | Second Probability | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| neitherProbability | Neither Probability | Required. Finite number. |
| atLeastOneProbability | At Least One Probability | Required. Finite number. |
{
"input": {
"firstProbability": 0.5,
"secondProbability": 0.25
},
"output": {
"neitherProbability": 0.375,
"atLeastOneProbability": 0.625
}
}Limitations and assumptions
- Independence is an assumption, not tested by the tool; dependent-event probabilities need joint information.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the complete joint model when independence or disjointness cannot be assumed. Evaluate a distribution on its actual support for CDF or likelihood questions, and keep absent categories distinct from explicitly listed zero-probability outcomes.
References
Similar or alternative tools
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