Finite Events
This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.
This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.
batch-20260918-finite-events · 2026-09-18 · 100 questions
This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.
1. Event Validity in a Finite Powerset Model
Let S={1, 2, 3}, with F=P(S) explicitly selected. Is E={2, 9} an event in this model?
View answer and explanation
No
9 is not in S, so E is not a subset of S.
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
2. Event Validity in a Finite Powerset Model
Let S={5, 6, 7}, with F=P(S) explicitly selected. Is E={5, 7} an event in this model?
View answer and explanation
Yes
Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S).
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
3. Event Validity in a Finite Powerset Model
Let S={9, 10, 11}, with F=P(S) explicitly selected. Is E={10, 17} an event in this model?
View answer and explanation
No
17 is not in S, so E is not a subset of S.
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
4. Event Validity in a Finite Powerset Model
Let S={13, 14, 15}, with F=P(S) explicitly selected. Is E={13, 15} an event in this model?
View answer and explanation
Yes
Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S).
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
5. Event Validity in a Finite Powerset Model
Let S={17, 18, 19}, with F=P(S) explicitly selected. Is E={18, 25} an event in this model?
View answer and explanation
No
25 is not in S, so E is not a subset of S.
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
6. Event Validity in a Finite Powerset Model
Let S={21, 22, 23}, with F=P(S) explicitly selected. Is E={21, 23} an event in this model?
View answer and explanation
Yes
Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S).
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
7. Event Validity in a Finite Powerset Model
Let S={25, 26, 27}, with F=P(S) explicitly selected. Is E={26, 33} an event in this model?
View answer and explanation
No
33 is not in S, so E is not a subset of S.
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
8. Event Validity in a Finite Powerset Model
Let S={29, 30, 31}, with F=P(S) explicitly selected. Is E={29, 31} an event in this model?
View answer and explanation
Yes
Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S).
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
9. Event Validity in a Finite Powerset Model
Let S={33, 34, 35}, with F=P(S) explicitly selected. Is E={34, 41} an event in this model?
View answer and explanation
No
41 is not in S, so E is not a subset of S.
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
10. Event Validity in a Finite Powerset Model
Let S={37, 38, 39}, with F=P(S) explicitly selected. Is E={37, 39} an event in this model?
View answer and explanation
Yes
Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S).
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
11. Event Validity in a Finite Powerset Model
Let S={41, 42, 43}, with F=P(S) explicitly selected. Is E={42, 49} an event in this model?
View answer and explanation
No
49 is not in S, so E is not a subset of S.
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
12. Event Validity in a Finite Powerset Model
Let S={45, 46, 47}, with F=P(S) explicitly selected. Is E={45, 47} an event in this model?
View answer and explanation
Yes
Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S).
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
13. Event Validity in a Finite Powerset Model
Let S={49, 50, 51}, with F=P(S) explicitly selected. Is E={50, 57} an event in this model?
View answer and explanation
No
57 is not in S, so E is not a subset of S.
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
14. Event Validity in a Finite Powerset Model
Let S={53, 54, 55}, with F=P(S) explicitly selected. Is E={53, 55} an event in this model?
View answer and explanation
Yes
Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S).
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
15. Event Validity in a Finite Powerset Model
Let S={57, 58, 59}, with F=P(S) explicitly selected. Is E={58, 65} an event in this model?
View answer and explanation
No
65 is not in S, so E is not a subset of S.
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
16. Event Validity in a Finite Powerset Model
Let S={61, 62, 63}, with F=P(S) explicitly selected. Is E={61, 63} an event in this model?
View answer and explanation
Yes
Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S).
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
17. Event Validity in a Finite Powerset Model
Let S={65, 66, 67}, with F=P(S) explicitly selected. Is E={66, 73} an event in this model?
View answer and explanation
No
73 is not in S, so E is not a subset of S.
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
18. Event Validity in a Finite Powerset Model
Let S={69, 70, 71}, with F=P(S) explicitly selected. Is E={69, 71} an event in this model?
View answer and explanation
Yes
Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S).
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
19. Event Validity in a Finite Powerset Model
Let S={73, 74, 75}, with F=P(S) explicitly selected. Is E={74, 81} an event in this model?
View answer and explanation
No
81 is not in S, so E is not a subset of S.
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
20. Event Validity in a Finite Powerset Model
Let S={77, 78, 79}, with F=P(S) explicitly selected. Is E={77, 79} an event in this model?
View answer and explanation
Yes
Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S).
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
21. Event Validity in a Finite Powerset Model
Let S={81, 82, 83}, with F=P(S) explicitly selected. Is E={82, 89} an event in this model?
View answer and explanation
No
89 is not in S, so E is not a subset of S.
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
22. Event Validity in a Finite Powerset Model
Let S={85, 86, 87}, with F=P(S) explicitly selected. Is E={85, 87} an event in this model?
View answer and explanation
Yes
Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S).
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
23. Event Validity in a Finite Powerset Model
Let S={89, 90, 91}, with F=P(S) explicitly selected. Is E={90, 97} an event in this model?
View answer and explanation
No
97 is not in S, so E is not a subset of S.
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
24. Event Validity in a Finite Powerset Model
Let S={93, 94, 95}, with F=P(S) explicitly selected. Is E={93, 95} an event in this model?
View answer and explanation
Yes
Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S).
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
25. Event Validity in a Finite Powerset Model
Let S={97, 98, 99}, with F=P(S) explicitly selected. Is E={98, 105} an event in this model?
View answer and explanation
No
105 is not in S, so E is not a subset of S.
Reviewed step-by-step derivation
Event · qf-finite-event-subset-validity · candidate
26. Outcome Versus Event
Let S={1, 2, 3} and F=P(S). 1 is a single outcome, while {1} is an event. Is the role of 1 “event set”?
View answer and explanation
No
1 is an element of S; {1} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
27. Outcome Versus Event
Let S={5, 6, 7} and F=P(S). 6 is a single outcome, while {6} is an event. Is the role of 6 “event set”?
View answer and explanation
No
6 is an element of S; {6} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
28. Outcome Versus Event
Let S={9, 10, 11} and F=P(S). 11 is a single outcome, while {11} is an event. Is the role of 11 “event set”?
View answer and explanation
No
11 is an element of S; {11} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
29. Outcome Versus Event
Let S={13, 14, 15} and F=P(S). 13 is a single outcome, while {13} is an event. Is the role of 13 “event set”?
View answer and explanation
No
13 is an element of S; {13} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
30. Outcome Versus Event
Let S={17, 18, 19} and F=P(S). 18 is a single outcome, while {18} is an event. Is the role of 18 “event set”?
View answer and explanation
No
18 is an element of S; {18} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
31. Outcome Versus Event
Let S={21, 22, 23} and F=P(S). 23 is a single outcome, while {23} is an event. Is the role of 23 “event set”?
View answer and explanation
No
23 is an element of S; {23} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
32. Outcome Versus Event
Let S={25, 26, 27} and F=P(S). 25 is a single outcome, while {25} is an event. Is the role of 25 “event set”?
View answer and explanation
No
25 is an element of S; {25} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
33. Outcome Versus Event
Let S={29, 30, 31} and F=P(S). 30 is a single outcome, while {30} is an event. Is the role of 30 “event set”?
View answer and explanation
No
30 is an element of S; {30} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
34. Outcome Versus Event
Let S={33, 34, 35} and F=P(S). 35 is a single outcome, while {35} is an event. Is the role of 35 “event set”?
View answer and explanation
No
35 is an element of S; {35} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
35. Outcome Versus Event
Let S={37, 38, 39} and F=P(S). 37 is a single outcome, while {37} is an event. Is the role of 37 “event set”?
View answer and explanation
No
37 is an element of S; {37} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
36. Outcome Versus Event
Let S={41, 42, 43} and F=P(S). 42 is a single outcome, while {42} is an event. Is the role of 42 “event set”?
View answer and explanation
No
42 is an element of S; {42} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
37. Outcome Versus Event
Let S={45, 46, 47} and F=P(S). 47 is a single outcome, while {47} is an event. Is the role of 47 “event set”?
View answer and explanation
No
47 is an element of S; {47} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
38. Outcome Versus Event
Let S={49, 50, 51} and F=P(S). 49 is a single outcome, while {49} is an event. Is the role of 49 “event set”?
View answer and explanation
No
49 is an element of S; {49} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
39. Outcome Versus Event
Let S={53, 54, 55} and F=P(S). 54 is a single outcome, while {54} is an event. Is the role of 54 “event set”?
View answer and explanation
No
54 is an element of S; {54} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
40. Outcome Versus Event
Let S={57, 58, 59} and F=P(S). 59 is a single outcome, while {59} is an event. Is the role of 59 “event set”?
View answer and explanation
No
59 is an element of S; {59} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
41. Outcome Versus Event
Let S={61, 62, 63} and F=P(S). 61 is a single outcome, while {61} is an event. Is the role of 61 “event set”?
View answer and explanation
No
61 is an element of S; {61} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
42. Outcome Versus Event
Let S={65, 66, 67} and F=P(S). 66 is a single outcome, while {66} is an event. Is the role of 66 “event set”?
View answer and explanation
No
66 is an element of S; {66} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
43. Outcome Versus Event
Let S={69, 70, 71} and F=P(S). 71 is a single outcome, while {71} is an event. Is the role of 71 “event set”?
View answer and explanation
No
71 is an element of S; {71} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
44. Outcome Versus Event
Let S={73, 74, 75} and F=P(S). 73 is a single outcome, while {73} is an event. Is the role of 73 “event set”?
View answer and explanation
No
73 is an element of S; {73} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
45. Outcome Versus Event
Let S={77, 78, 79} and F=P(S). 78 is a single outcome, while {78} is an event. Is the role of 78 “event set”?
View answer and explanation
No
78 is an element of S; {78} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
46. Outcome Versus Event
Let S={81, 82, 83} and F=P(S). 83 is a single outcome, while {83} is an event. Is the role of 83 “event set”?
View answer and explanation
No
83 is an element of S; {83} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
47. Outcome Versus Event
Let S={85, 86, 87} and F=P(S). 85 is a single outcome, while {85} is an event. Is the role of 85 “event set”?
View answer and explanation
No
85 is an element of S; {85} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
48. Outcome Versus Event
Let S={89, 90, 91} and F=P(S). 90 is a single outcome, while {90} is an event. Is the role of 90 “event set”?
View answer and explanation
No
90 is an element of S; {90} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
49. Outcome Versus Event
Let S={93, 94, 95} and F=P(S). 95 is a single outcome, while {95} is an event. Is the role of 95 “event set”?
View answer and explanation
No
95 is an element of S; {95} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
50. Outcome Versus Event
Let S={97, 98, 99} and F=P(S). 97 is a single outcome, while {97} is an event. Is the role of 97 “event set”?
View answer and explanation
No
97 is an element of S; {97} is the event written as a set of outcomes.
Reviewed step-by-step derivation
Event · qf-outcome-versus-event-role · candidate
51. Occurrence of a Finite Event
Let S={1, 2, 3}, F=P(S), and E={2}. The observed outcome is 1. Does E occur?
View answer and explanation
No
1 does not belong to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
52. Occurrence of a Finite Event
Let S={5, 6, 7}, F=P(S), and E={5, 7}. The observed outcome is 5. Does E occur?
View answer and explanation
Yes
5 belongs to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
53. Occurrence of a Finite Event
Let S={9, 10, 11}, F=P(S), and E={10}. The observed outcome is 9. Does E occur?
View answer and explanation
No
9 does not belong to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
54. Occurrence of a Finite Event
Let S={13, 14, 15}, F=P(S), and E={13, 15}. The observed outcome is 13. Does E occur?
View answer and explanation
Yes
13 belongs to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
55. Occurrence of a Finite Event
Let S={17, 18, 19}, F=P(S), and E={18}. The observed outcome is 17. Does E occur?
View answer and explanation
No
17 does not belong to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
56. Occurrence of a Finite Event
Let S={21, 22, 23}, F=P(S), and E={21, 23}. The observed outcome is 21. Does E occur?
View answer and explanation
Yes
21 belongs to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
57. Occurrence of a Finite Event
Let S={25, 26, 27}, F=P(S), and E={26}. The observed outcome is 25. Does E occur?
View answer and explanation
No
25 does not belong to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
58. Occurrence of a Finite Event
Let S={29, 30, 31}, F=P(S), and E={29, 31}. The observed outcome is 29. Does E occur?
View answer and explanation
Yes
29 belongs to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
59. Occurrence of a Finite Event
Let S={33, 34, 35}, F=P(S), and E={34}. The observed outcome is 33. Does E occur?
View answer and explanation
No
33 does not belong to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
60. Occurrence of a Finite Event
Let S={37, 38, 39}, F=P(S), and E={37, 39}. The observed outcome is 37. Does E occur?
View answer and explanation
Yes
37 belongs to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
61. Occurrence of a Finite Event
Let S={41, 42, 43}, F=P(S), and E={42}. The observed outcome is 41. Does E occur?
View answer and explanation
No
41 does not belong to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
62. Occurrence of a Finite Event
Let S={45, 46, 47}, F=P(S), and E={45, 47}. The observed outcome is 45. Does E occur?
View answer and explanation
Yes
45 belongs to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
63. Occurrence of a Finite Event
Let S={49, 50, 51}, F=P(S), and E={50}. The observed outcome is 49. Does E occur?
View answer and explanation
No
49 does not belong to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
64. Occurrence of a Finite Event
Let S={53, 54, 55}, F=P(S), and E={53, 55}. The observed outcome is 53. Does E occur?
View answer and explanation
Yes
53 belongs to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
65. Occurrence of a Finite Event
Let S={57, 58, 59}, F=P(S), and E={58}. The observed outcome is 57. Does E occur?
View answer and explanation
No
57 does not belong to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
66. Occurrence of a Finite Event
Let S={61, 62, 63}, F=P(S), and E={61, 63}. The observed outcome is 61. Does E occur?
View answer and explanation
Yes
61 belongs to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
67. Occurrence of a Finite Event
Let S={65, 66, 67}, F=P(S), and E={66}. The observed outcome is 65. Does E occur?
View answer and explanation
No
65 does not belong to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
68. Occurrence of a Finite Event
Let S={69, 70, 71}, F=P(S), and E={69, 71}. The observed outcome is 69. Does E occur?
View answer and explanation
Yes
69 belongs to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
69. Occurrence of a Finite Event
Let S={73, 74, 75}, F=P(S), and E={74}. The observed outcome is 73. Does E occur?
View answer and explanation
No
73 does not belong to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
70. Occurrence of a Finite Event
Let S={77, 78, 79}, F=P(S), and E={77, 79}. The observed outcome is 77. Does E occur?
View answer and explanation
Yes
77 belongs to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
71. Occurrence of a Finite Event
Let S={81, 82, 83}, F=P(S), and E={82}. The observed outcome is 81. Does E occur?
View answer and explanation
No
81 does not belong to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
72. Occurrence of a Finite Event
Let S={85, 86, 87}, F=P(S), and E={85, 87}. The observed outcome is 85. Does E occur?
View answer and explanation
Yes
85 belongs to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
73. Occurrence of a Finite Event
Let S={89, 90, 91}, F=P(S), and E={90}. The observed outcome is 89. Does E occur?
View answer and explanation
No
89 does not belong to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
74. Occurrence of a Finite Event
Let S={93, 94, 95}, F=P(S), and E={93, 95}. The observed outcome is 93. Does E occur?
View answer and explanation
Yes
93 belongs to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
75. Occurrence of a Finite Event
Let S={97, 98, 99}, F=P(S), and E={98}. The observed outcome is 97. Does E occur?
View answer and explanation
No
97 does not belong to E. No probability is assigned in this question.
Reviewed step-by-step derivation
Event · qf-finite-event-occurrence · candidate
76. Cardinality of a Finite Event
Let S={1, 2, 3}, F=P(S), and E={2}. What is the cardinality of E?
View answer and explanation
1
E contains 1 distinct outcome. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
77. Cardinality of a Finite Event
Let S={5, 6, 7}, F=P(S), and E={5, 7}. What is the cardinality of E?
View answer and explanation
2
E contains 2 distinct outcomes. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
78. Cardinality of a Finite Event
Let S={9, 10, 11}, F=P(S), and E={10}. What is the cardinality of E?
View answer and explanation
1
E contains 1 distinct outcome. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
79. Cardinality of a Finite Event
Let S={13, 14, 15}, F=P(S), and E={13, 15}. What is the cardinality of E?
View answer and explanation
2
E contains 2 distinct outcomes. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
80. Cardinality of a Finite Event
Let S={17, 18, 19}, F=P(S), and E={18}. What is the cardinality of E?
View answer and explanation
1
E contains 1 distinct outcome. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
81. Cardinality of a Finite Event
Let S={21, 22, 23}, F=P(S), and E={21, 23}. What is the cardinality of E?
View answer and explanation
2
E contains 2 distinct outcomes. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
82. Cardinality of a Finite Event
Let S={25, 26, 27}, F=P(S), and E={26}. What is the cardinality of E?
View answer and explanation
1
E contains 1 distinct outcome. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
83. Cardinality of a Finite Event
Let S={29, 30, 31}, F=P(S), and E={29, 31}. What is the cardinality of E?
View answer and explanation
2
E contains 2 distinct outcomes. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
84. Cardinality of a Finite Event
Let S={33, 34, 35}, F=P(S), and E={34}. What is the cardinality of E?
View answer and explanation
1
E contains 1 distinct outcome. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
85. Cardinality of a Finite Event
Let S={37, 38, 39}, F=P(S), and E={37, 39}. What is the cardinality of E?
View answer and explanation
2
E contains 2 distinct outcomes. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
86. Cardinality of a Finite Event
Let S={41, 42, 43}, F=P(S), and E={42}. What is the cardinality of E?
View answer and explanation
1
E contains 1 distinct outcome. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
87. Cardinality of a Finite Event
Let S={45, 46, 47}, F=P(S), and E={45, 47}. What is the cardinality of E?
View answer and explanation
2
E contains 2 distinct outcomes. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
88. Cardinality of a Finite Event
Let S={49, 50, 51}, F=P(S), and E={50}. What is the cardinality of E?
View answer and explanation
1
E contains 1 distinct outcome. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
89. Cardinality of a Finite Event
Let S={53, 54, 55}, F=P(S), and E={53, 55}. What is the cardinality of E?
View answer and explanation
2
E contains 2 distinct outcomes. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
90. Cardinality of a Finite Event
Let S={57, 58, 59}, F=P(S), and E={58}. What is the cardinality of E?
View answer and explanation
1
E contains 1 distinct outcome. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
91. Cardinality of a Finite Event
Let S={61, 62, 63}, F=P(S), and E={61, 63}. What is the cardinality of E?
View answer and explanation
2
E contains 2 distinct outcomes. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
92. Cardinality of a Finite Event
Let S={65, 66, 67}, F=P(S), and E={66}. What is the cardinality of E?
View answer and explanation
1
E contains 1 distinct outcome. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
93. Cardinality of a Finite Event
Let S={69, 70, 71}, F=P(S), and E={69, 71}. What is the cardinality of E?
View answer and explanation
2
E contains 2 distinct outcomes. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
94. Cardinality of a Finite Event
Let S={73, 74, 75}, F=P(S), and E={74}. What is the cardinality of E?
View answer and explanation
1
E contains 1 distinct outcome. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
95. Cardinality of a Finite Event
Let S={77, 78, 79}, F=P(S), and E={77, 79}. What is the cardinality of E?
View answer and explanation
2
E contains 2 distinct outcomes. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
96. Cardinality of a Finite Event
Let S={81, 82, 83}, F=P(S), and E={82}. What is the cardinality of E?
View answer and explanation
1
E contains 1 distinct outcome. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
97. Cardinality of a Finite Event
Let S={85, 86, 87}, F=P(S), and E={85, 87}. What is the cardinality of E?
View answer and explanation
2
E contains 2 distinct outcomes. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
98. Cardinality of a Finite Event
Let S={89, 90, 91}, F=P(S), and E={90}. What is the cardinality of E?
View answer and explanation
1
E contains 1 distinct outcome. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
99. Cardinality of a Finite Event
Let S={93, 94, 95}, F=P(S), and E={93, 95}. What is the cardinality of E?
View answer and explanation
2
E contains 2 distinct outcomes. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
100. Cardinality of a Finite Event
Let S={97, 98, 99}, F=P(S), and E={98}. What is the cardinality of E?
View answer and explanation
1
E contains 1 distinct outcome. This is a cardinality, not a probability.
Reviewed step-by-step derivation
Event · qf-finite-event-cardinality · candidate
Canonical question JSONL · English JSONL · Validation report