Description
Return first*(1-second)+second*(1-first) for two valid probabilities.
Event probabilities and probability masses lie between zero and one. Marginals, intersections, conditioning events, and endpoint atoms describe different quantities. A probability bound or local consistency check can constrain a model without specifying its complete distribution or dependence structure.
Return first*(1-second)+second*(1-first) for two valid probabilities.
When to use this tool
Use Independent Event Xor Probability when you need the stated event identity, boundary policy, distribution component, or local feasibility check.
How to use the tool and how it works
- Enter first, second. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read probability. Use the output convention below.
Return first*(1-second)+second*(1-first) for two valid probabilities.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| first | First | Required. Finite number; minimum 0; maximum 1. |
| second | Second | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| probability | Dimensionless probability from zero through one. | Required. Finite number. |
{
"input": {
"first": 0.25,
"second": 0.5
},
"output": {
"probability": 0.5
}
}Limitations and assumptions
- The exclusive-or probability uses independence. Marginal probabilities alone are insufficient when the two events are dependent.
- 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. Signed zero is exported as zero.
Alternative or Complementary methods
Use a full probability table or distribution when a local mass, bound, or identity is insufficient. Specify dependence, conditioning, support order, and endpoint policy before combining terms.
References
Similar or alternative tools
- Rare Event Probability Expm1 Crosswalk
Return eventProbability=-expm1(logSurvival) for a nonpositive finite natural logarithm of survival probability.
- Atom Probability Lower Slack
For probability and suppliedLowerBound within zero through one return slack=probability-suppliedLowerBound and feasible=(probability>=suppliedLowerBound).