# Question 27108: Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

[Return to catalogue page 136](https://ocme.evemisslab.com/en/questions/page/136/)

[← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations/#q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0083)

This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth.

R0053-27108 · q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0083



## Original question and givens

Use mode=invalid_procedure and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[8,10],[2,10]],[[2,10],[8,10]]],"intervals":[[8,7],[8,8]]}. Give (mode, procedure_valid, validation_error, procedure_qualification_claim).


- G001 — Use mode=invalid_procedure and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[8,10],[2,10]],[[2,10],[8,10]]],"intervals":[[8,7],[8,8]]}. Give (mode, procedure_valid, validation_error, procedure_qualification_claim).





## Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.


- [mko-finite-confidence-interval-coverage](https://ocme.evemisslab.com/en/mko/mko-finite-confidence-interval-coverage/)





## Step-by-step derivation

S001 · impliesBefore

source roles = [ci-interpretation-boundary]

After

derived = [[mode, procedure_valid, validation_error, procedure_qualification_claim]]

Conditions: none

List the complete source field order and mode-specific roles without JavaScript or answer-shape inference;No,undefined and infinity retain their distinct meanings.

Step identifiers and dependenciesRule: source_ordered_fields_without_JS · Uses: G001





S002 · impliesBefore

source roles = [{'theta_values': [0, 1], 'samples': ['a', 'b'], 'probability_rows': [[[8, 10], [2, 10]], [[2, 10], [8, 10]]], 'intervals': [[8, 7], [8, 8]]}]

After

derived = [No, interval lower endpoint exceeds upper endpoint, No]

Conditions: none

Retain the actual FIRST validation error in source order,not one generic False for missing rows,unnormalized laws or bad intervals.This mode does not calculate coverage for an unqualified procedure.

Step identifiers and dependenciesRule: CI_invalid_procedure_ACTUAL_first_source_validation_error · Uses: G001, S001









## Reverse checks


- S002 · premise_and_result_audit — Reverse-check the complete original data,step operands and premises;finite checks,conditional named-theorem use and general formal proof remain distinct.
- S001 · premise_and_result_audit — Reverse-check the complete original data,step operands and premises;finite checks,conditional named-theorem use and general formal proof remain distinct.





## Result

(invalid_procedure, No, interval lower endpoint exceeds upper endpoint, No)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.





## This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.

Source hashes and review receipts
- input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
- original question SHA-256: f296e706a4abd09d02660e1c81a3032a6a525e2ccfedd37868c5265cc95e4881
- candidate record SHA-256: 09c75655a6b7ac2e3f0fb30c66a6f1c64dcd447a3e3aef926eb3be37b15cca08
- semantic review receipt SHA-256: 1b7a62514347b82518305d5feb4369a52d7d44c442a0f2b131e9eb3cd7b45f62
- question-first witness SHA-256: 79dc2a1077081f3ea2a03f75e32778163bf05e814cdf4c29ed86e567295f9ee1
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0083.json)