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