Description
Return conditionalProbability=jointProbability/conditioningProbability, impliedComplement=1-conditionalProbability, and gap=suppliedComplement-impliedComplement.
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 conditionalProbability=jointProbability/conditioningProbability, impliedComplement=1-conditionalProbability, and gap=suppliedComplement-impliedComplement.
When to use this tool
Use Conditional Event Complement Gap 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 jointProbability, conditioningProbability, suppliedComplement. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read conditionalProbability, impliedComplement, gap. Use the output convention below.
Require positive conditioningProbability and jointProbability no greater than it, with all probabilities in zero through one. Return conditionalProbability=jointProbability/conditioningProbability, impliedComplement=1-conditionalProbability, and gap=suppliedComplement-impliedComplement.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| jointProbability | Joint Probability | Required. Finite number; minimum 0; maximum 1. |
| conditioningProbability | Conditioning Probability | Required. Finite number; minimum 0; maximum 1; strictly above 0. |
| suppliedComplement | Supplied Complement | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| conditionalProbability | Conditional Probability | Required. Finite number. |
| impliedComplement | Implied Complement | Required. Finite number. |
| gap | Signed difference under the stated formula and measurement unit. | Required. Finite number. |
{
"input": {
"jointProbability": 0.2,
"conditioningProbability": 0.5,
"suppliedComplement": 0.7
},
"output": {
"conditionalProbability": 0.4,
"impliedComplement": 0.6,
"gap": 0.09999999999999998
}
}Limitations and assumptions
- Gap is signed and uses fraction units. The supplied complement is checked arithmetically rather than established from event definitions or observations.
- 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
- Probability: Event Complement Interval Bounds
Transform a closed probability-uncertainty interval through the decreasing complement map, reversing endpoints.
- Event Odds Complement Factor
For probability strictly between zero and one return eventOdds=p/(1-p), complementOdds=(1-p)/p, and product=1.