# Question 6060: Typed Observations, Event Occurrence, and First Hit

[Return to catalogue page 31](https://ocme.evemisslab.com/en/questions/page/31/)

[← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20261009-advance-20261013-r06-event-foundations/#q-20261009-advance-20261013-r06-event-0085)

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.

R0011-06060 · q-20261009-advance-20261013-r06-event-0085



## Original question and givens

S=Fin(3)={0,…,2}; the event family is explicitly F=P(S). E=[1], ordered outcomes=[100, 1, 102]. Give (sample-eligibility mask, True/False/invalid-outcome occurrence list, first legal E hit’s zero-based index or none).


- G001 — S=Fin(3)={0,…,2}; the event family is explicitly F=P(S). E=[1], ordered outcomes=[100, 1, 102]. Give (sample-eligibility mask, True/False/invalid-outcome occurrence list, first legal E hit’s zero-based index or none).





## 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-event](https://ocme.evemisslab.com/en/mko/mko-event/)





## Step-by-step derivation

S001 · impliesBefore

S=Fin(3)=[0, 1, 2];declared event model=full_powerset

After

finite S alone does not specify its event family or a probability law

Conditions: none

A finite sample space does not automatically choose F=P(S).Use the declared event family;set data alone give no probabilities,equiprobability or independence.

Step identifiers and dependenciesRule: declared_finite_event_family · Uses: G001





S002 · impliesBefore

observation position=0;candidate outcome=100;inside S=No

After

event occurrence=invalid sample

Conditions: none

First check whether the outcome lies in S,then event membership.An outside candidate is not assigned False occurrence;observation position and outcome value differ.

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





S003 · impliesBefore

observation position=1;candidate outcome=1;inside S=Yes

After

event occurrence=True

Conditions: none

First check whether the outcome lies in S,then event membership.An outside candidate is not assigned False occurrence;observation position and outcome value differ.

Step identifiers and dependenciesRule: typed_event_occurrence_row · Uses: G001, S002





S004 · impliesBefore

observation position=2;candidate outcome=102;inside S=No

After

event occurrence=invalid sample

Conditions: none

First check whether the outcome lies in S,then event membership.An outside candidate is not assigned False occurrence;observation position and outcome value differ.

Step identifiers and dependenciesRule: typed_event_occurrence_row · Uses: G001, S003





S005 · impliesBefore

legal event hits among ordered candidates;E=[1]

After

first hit position=1

Conditions: none

Return the first0-based position of a legal E-hit in the ordered list;an empty list or no hit gives none,without invented observations.

Step identifiers and dependenciesRule: first_legal_event_hit_position · Uses: G001, S004









## Reverse checks


- S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.





## Result

([No, Yes, No], [invalid-outcome, True, invalid-outcome], 1)

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: 122c3507d1dbb208ce3af94adb5712f535564e5f16b409909e6e097cfeb00953
- candidate record SHA-256: 5a2b1ba27cff044190f021f48491604f69febef6013bb62d8615b2aba6940f7b
- semantic review receipt SHA-256: b9bbc1c947f477a9c4bb5a579368ac5265f2da4572ce612c30f3633ecaf4ae80
- question-first witness SHA-256: 93f720df3ab3af13a792a3e6b443728e3c2a56276df839911f36569333236c55
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261009-advance-20261013-r06-event-0085.json)