Description
For valid marginal probabilities and an intersection within their exact feasible bounds, return union=left+right-intersection and correction=-intersection.
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.
For valid marginal probabilities and an intersection within their exact feasible bounds, return union=left+right-intersection and correction=-intersection.
When to use this tool
Use Event Union Disjointness Correction 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 left, right, intersection. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read union, correction. Use the output convention below.
For valid marginal probabilities and an intersection within their exact feasible bounds, return union=left+right-intersection and correction=-intersection.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| left | Left | Required. Finite number; minimum 0; maximum 1. |
| right | Right | Required. Finite number; minimum 0; maximum 1. |
| intersection | Intersection | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| union | Union | Required. Finite number. |
| correction | Correction | Required. Finite number. |
{
"input": {
"left": 0.5,
"right": 0.5,
"intersection": 0.25
},
"output": {
"union": 0.75,
"correction": -0.25
}
}Limitations and assumptions
- The negative correction removes overlap counted twice. Event definitions and the supplied intersection still need to be consistent; independence is not assumed.
- 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
- Finite Event Disjoint Union Membership Flag
Return inUnion=inFirst OR inSecond and disjointAtElement=NOT(inFirst AND inSecond) for the supplied membership flags.
- Censored Event Boundary Mass
Distinguish P(X<t) from P(X<=t) using supplied left-limit and endpoint CDF values.