Probability Basics Calculator

Inspectable records

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