Source: https://guthlabs.ai/docs/instruments/probability-basics-calculator/

instrument / verified-clean

# Probability Basics Calculator

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/probability-basics-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/probability-basics-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/probability-basics-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/probability-basics-calculator/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Mathematics — arithmetic through advanced (algebra, matrices, calculus, sequences/series, number theory, combinatorics, graphing, complex numbers, geometry, logic, sets)

**Tranche**: tranche-4

**Evidence ID**: t4-129

**Ledger rows**: 1

No ledger note is attached.

## Review findings

NEEDS_REVIEW because the input description 'probabilities/outcomes table' is ambiguous: it does not define the schema for event probabilities, intersections, conditional probabilities, Bayes denominators, or outcome-probability pairs. The specification also does not define validation, normalization, rounding tolerance, or behavior for P(B)=0.

### Formula and scope findings

- The three stated formulas are standard and correct under their usual conditions.

- The specification does not state required probability constraints: every probability must lie in [0,1], event probabilities must be mutually consistent, and a discrete distribution used for expected value must have nonnegative probabilities summing to 1.

- The conditional-probability and Bayes formulas require P(B)>0; this domain constraint is not stated.

- For expected value, the formula requires a finite distribution or a convergent countably infinite series; that scope is not specified.

### Unit assumptions

- Probabilities are dimensionless decimal values or fractions in the range [0,1].

- P(A∩B), P(B|A), P(A), and P(B) must use the same probability representation and event definitions.

- Outcomes x have compatible numeric units; E[X] has the same units as x.

- For an outcome-probability table, probabilities are assumed to be nonnegative and sum exactly to 1, subject to documented rounding tolerance.

## Boundary hardening

### Recorded hazards

- Division by zero occurs when P(B)=0; the calculator must reject or clearly report an undefined conditional probability or Bayes result.

- Invalid probabilities below 0 or above 1 must be rejected.

- Inconsistent event inputs can produce misleading results unless bounds such as P(A∩B)≤P(A) and P(A∩B)≤P(B) are enforced when the corresponding values are supplied.

- Expected-value tables with probabilities that do not sum to 1 require rejection or explicit normalization behavior; normalization is not specified.

- Rounding can make a probability table sum slightly above or below 1, so the accepted tolerance is unspecified.

- Infinite or very large outcome tables can make expected-value computation divergent, overflow, or lose precision.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "P_A_intersection_B": 0.18,
    "P_B": 0.3
  },
  "expected_outputs": {
    "P_A_given_B": 0.6
  },
  "working": "P(A|B)=P(A∩B)/P(B)=0.18/0.30=0.60."
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche4/tranche4-results.json`