# Finite Conditional Laws and Candidate Defects

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-20261008-advance-20261010-r04-conditional-probability-foundations · 2026-10-08 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.



## 1. Intersection and Conditioning-Event Probabilities

S={0,…,2}, F=P(S), masses=[0, 1, 2], D=3, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[], B=[1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(0/1, 1/3)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (0/1, 1/3).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0001/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 2. Intersection and Conditioning-Event Probabilities

S={0,…,2}, F=P(S), masses=[1, 0, 0], D=1, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(1/1, 1/1)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (1/1, 1/1).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0002/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 3. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[2, 1, 2, 0], D=5, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(2/5, 3/5)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (2/5, 3/5).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0003/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 4. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[3, 1, 2, 0], D=6, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(1/2, 2/3)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (1/2, 2/3).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0004/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 5. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[4, 1, 2, 0], D=7, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(4/7, 5/7)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (4/7, 5/7).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0005/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 6. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[5, 1, 2, 0], D=8, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(5/8, 3/4)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (5/8, 3/4).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0006/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 7. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[6, 1, 2, 0], D=9, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(2/3, 7/9)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (2/3, 7/9).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0007/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 8. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[7, 1, 2, 0], D=10, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(7/10, 4/5)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (7/10, 4/5).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0008/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 9. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[8, 1, 2, 0], D=11, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(8/11, 9/11)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (8/11, 9/11).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0009/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 10. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[9, 1, 2, 0], D=12, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(3/4, 5/6)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (3/4, 5/6).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0010/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 11. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[10, 1, 2, 0], D=13, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(10/13, 11/13)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (10/13, 11/13).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0011/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 12. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[11, 1, 2, 0], D=14, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(11/14, 6/7)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (11/14, 6/7).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0012/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 13. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[12, 1, 2, 0], D=15, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(4/5, 13/15)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (4/5, 13/15).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0013/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 14. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[13, 1, 2, 0], D=16, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(13/16, 7/8)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (13/16, 7/8).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0014/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 15. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[14, 1, 2, 0], D=17, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(14/17, 15/17)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (14/17, 15/17).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0015/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 16. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[15, 1, 2, 0], D=18, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(5/6, 8/9)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (5/6, 8/9).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0016/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 17. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[16, 1, 2, 0], D=19, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(16/19, 17/19)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (16/19, 17/19).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0017/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 18. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[17, 1, 2, 0], D=20, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(17/20, 9/10)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (17/20, 9/10).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0018/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 19. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[18, 1, 2, 0], D=21, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(6/7, 19/21)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (6/7, 19/21).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0019/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 20. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[19, 1, 2, 0], D=22, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(19/22, 10/11)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (19/22, 10/11).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0020/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 21. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[20, 1, 2, 0], D=23, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(20/23, 21/23)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (20/23, 21/23).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0021/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 22. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[21, 1, 2, 0], D=24, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(7/8, 11/12)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (7/8, 11/12).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0022/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 23. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[22, 1, 2, 0], D=25, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(22/25, 23/25)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (22/25, 23/25).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0023/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 24. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[23, 1, 2, 0], D=26, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(23/26, 12/13)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (23/26, 12/13).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0024/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 25. Intersection and Conditioning-Event Probabilities

S={0,…,3}, F=P(S), masses=[24, 1, 2, 0], D=27, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Give (P(A∩B), P(B)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(8/9, 25/27)

Sum each event mass and divide separately by D; this question does not yet divide the two probabilities, and nonempty B alone would not imply positive probability. The exact result, retaining the requested order, is (8/9, 25/27).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0025/)

Conditional probability in finite models · qf-density10-conditional-masses-pair · candidate





## 26. Both Conditional-Probability Directions

S={0,…,1}, F=P(S), masses=[1, 2], D=3, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0], B=[1], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(0/1, 0/1)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (0/1, 0/1).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0026/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 27. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[1, 0, 2], D=3, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0], B=[0, 1], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(1/1, 1/1)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (1/1, 1/1).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0027/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 28. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[2, 1, 2], D=5, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(1/2, 2/3)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (1/2, 2/3).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0028/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 29. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[3, 1, 2], D=6, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(3/5, 3/4)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (3/5, 3/4).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0029/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 30. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[4, 1, 2], D=7, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(2/3, 4/5)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (2/3, 4/5).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0030/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 31. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[5, 1, 2], D=8, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(5/7, 5/6)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (5/7, 5/6).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0031/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 32. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[6, 1, 2], D=9, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(3/4, 6/7)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (3/4, 6/7).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0032/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 33. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[7, 1, 2], D=10, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(7/9, 7/8)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (7/9, 7/8).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0033/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 34. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[8, 1, 2], D=11, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(4/5, 8/9)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (4/5, 8/9).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0034/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 35. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[9, 1, 2], D=12, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(9/11, 9/10)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (9/11, 9/10).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0035/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 36. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[10, 1, 2], D=13, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(5/6, 10/11)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (5/6, 10/11).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0036/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 37. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[11, 1, 2], D=14, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(11/13, 11/12)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (11/13, 11/12).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0037/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 38. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[12, 1, 2], D=15, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(6/7, 12/13)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (6/7, 12/13).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0038/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 39. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[13, 1, 2], D=16, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(13/15, 13/14)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (13/15, 13/14).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0039/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 40. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[14, 1, 2], D=17, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(7/8, 14/15)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (7/8, 14/15).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0040/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 41. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[15, 1, 2], D=18, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(15/17, 15/16)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (15/17, 15/16).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0041/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 42. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[16, 1, 2], D=19, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(8/9, 16/17)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (8/9, 16/17).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0042/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 43. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[17, 1, 2], D=20, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(17/19, 17/18)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (17/19, 17/18).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0043/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 44. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[18, 1, 2], D=21, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(9/10, 18/19)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (9/10, 18/19).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0044/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 45. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[19, 1, 2], D=22, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(19/21, 19/20)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (19/21, 19/20).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0045/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 46. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[20, 1, 2], D=23, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(10/11, 20/21)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (10/11, 20/21).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0046/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 47. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[21, 1, 2], D=24, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(21/23, 21/22)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (21/23, 21/22).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0047/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 48. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[22, 1, 2], D=25, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(11/12, 22/23)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (11/12, 22/23).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0048/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 49. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[23, 1, 2], D=26, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(23/25, 23/24)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (23/25, 23/24).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0049/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 50. Both Conditional-Probability Directions

S={0,…,2}, F=P(S), masses=[24, 1, 2], D=27, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 1], B=[0, 2], P(A)>0 and P(B)>0. Give (P(A|B), P(B|A)). Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation(12/13, 24/25)

Divide the shared intersection mass by the B mass and the A mass respectively; the two directions generally differ, and independence is not assumed. The exact result, retaining the requested order, is (12/13, 24/25).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0050/)

Conditional probability in finite models · qf-density10-conditional-directions-pair · candidate





## 51. Complete Pointwise Conditional Law

S={0,…,2}, F=P(S), masses=[0, 1, 2], D=3, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[1], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[0/1, 1/1, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [0/1, 1/1, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0051/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 52. Complete Pointwise Conditional Law

S={0,…,0}, F=P(S), masses=[1], D=1, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[1/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [1/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0052/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 53. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[2, 1, 2, 3], D=8, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[2/5, 1/5, 2/5, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [2/5, 1/5, 2/5, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0053/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 54. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[3, 1, 2, 3], D=9, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[1/2, 1/6, 1/3, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [1/2, 1/6, 1/3, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0054/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 55. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[4, 1, 2, 3], D=10, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[4/7, 1/7, 2/7, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [4/7, 1/7, 2/7, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0055/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 56. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[5, 1, 2, 3], D=11, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[5/8, 1/8, 1/4, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [5/8, 1/8, 1/4, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0056/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 57. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[6, 1, 2, 3], D=12, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[2/3, 1/9, 2/9, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [2/3, 1/9, 2/9, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0057/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 58. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[7, 1, 2, 3], D=13, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[7/10, 1/10, 1/5, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [7/10, 1/10, 1/5, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0058/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 59. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[8, 1, 2, 3], D=14, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[8/11, 1/11, 2/11, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [8/11, 1/11, 2/11, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0059/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 60. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[9, 1, 2, 3], D=15, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[3/4, 1/12, 1/6, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [3/4, 1/12, 1/6, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0060/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 61. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[10, 1, 2, 3], D=16, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[10/13, 1/13, 2/13, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [10/13, 1/13, 2/13, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0061/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 62. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[11, 1, 2, 3], D=17, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[11/14, 1/14, 1/7, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [11/14, 1/14, 1/7, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0062/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 63. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[12, 1, 2, 3], D=18, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[4/5, 1/15, 2/15, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [4/5, 1/15, 2/15, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0063/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 64. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[13, 1, 2, 3], D=19, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[13/16, 1/16, 1/8, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [13/16, 1/16, 1/8, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0064/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 65. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[14, 1, 2, 3], D=20, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[14/17, 1/17, 2/17, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [14/17, 1/17, 2/17, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0065/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 66. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[15, 1, 2, 3], D=21, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[5/6, 1/18, 1/9, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [5/6, 1/18, 1/9, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0066/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 67. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[16, 1, 2, 3], D=22, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[16/19, 1/19, 2/19, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [16/19, 1/19, 2/19, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0067/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 68. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[17, 1, 2, 3], D=23, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[17/20, 1/20, 1/10, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [17/20, 1/20, 1/10, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0068/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 69. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[18, 1, 2, 3], D=24, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[6/7, 1/21, 2/21, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [6/7, 1/21, 2/21, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0069/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 70. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[19, 1, 2, 3], D=25, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[19/22, 1/22, 1/11, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [19/22, 1/22, 1/11, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0070/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 71. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[20, 1, 2, 3], D=26, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[20/23, 1/23, 2/23, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [20/23, 1/23, 2/23, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0071/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 72. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[21, 1, 2, 3], D=27, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[7/8, 1/24, 1/12, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [7/8, 1/24, 1/12, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0072/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 73. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[22, 1, 2, 3], D=28, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[22/25, 1/25, 2/25, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [22/25, 1/25, 2/25, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0073/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 74. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[23, 1, 2, 3], D=29, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[23/26, 1/26, 1/13, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [23/26, 1/26, 1/13, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0074/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 75. Complete Pointwise Conditional Law

S={0,…,3}, F=P(S), masses=[24, 1, 2, 3], D=30, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. B=[0, 1, 2], P(B)>0. In index order from 0, list the conditional probability of every singleton given B, including zero terms outside B. Use exact reduced fractions with positive denominators, retaining /1 for integers.

View answer and explanation[8/9, 1/27, 2/27, 0/1]

For a point in B divide its mass by the total B mass; outside B use 0/1. The complete vector sums to one. The exact result, retaining the requested order, is [8/9, 1/27, 2/27, 0/1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0075/)

Conditional probability in finite models · qf-density10-conditional-point-law · candidate





## 76. Conditional Candidate Eligibility and Signed Defect

S={0,…,1}, F=P(S), masses=[1, 1], D=2, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0], B=[0, 1], P(B)>0. Candidate=1/2. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(Yes, 0/1)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (Yes, 0/1).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0076/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 77. Conditional Candidate Eligibility and Signed Defect

S={0,…,1}, F=P(S), masses=[1, 1], D=2, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0], B=[0, 1], P(B)>0. Candidate=-1/1. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(No, -3/2)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (No, -3/2).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0077/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 78. Conditional Candidate Eligibility and Signed Defect

S={0,…,1}, F=P(S), masses=[1, 1], D=2, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0], B=[0, 1], P(B)>0. Candidate=2/1. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(No, 3/2)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (No, 3/2).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0078/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 79. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[3, 1, 2, 0], D=6, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=3/4. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(Yes, 0/1)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (Yes, 0/1).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0079/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 80. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[4, 1, 2, 0], D=7, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=5/5. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(No, 1/5)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (No, 1/5).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0080/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 81. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[5, 1, 2, 0], D=8, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=4/6. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(No, -1/6)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (No, -1/6).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0081/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 82. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[6, 1, 2, 0], D=9, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=6/7. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(Yes, 0/1)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (Yes, 0/1).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0082/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 83. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[7, 1, 2, 0], D=10, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=8/8. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(No, 1/8)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (No, 1/8).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0083/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 84. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[8, 1, 2, 0], D=11, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=7/9. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(No, -1/9)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (No, -1/9).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0084/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 85. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[9, 1, 2, 0], D=12, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=9/10. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(Yes, 0/1)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (Yes, 0/1).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0085/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 86. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[10, 1, 2, 0], D=13, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=11/11. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(No, 1/11)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (No, 1/11).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0086/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 87. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[11, 1, 2, 0], D=14, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=10/12. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(No, -1/12)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (No, -1/12).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0087/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 88. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[12, 1, 2, 0], D=15, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=12/13. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(Yes, 0/1)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (Yes, 0/1).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0088/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 89. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[13, 1, 2, 0], D=16, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=14/14. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(No, 1/14)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (No, 1/14).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0089/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 90. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[14, 1, 2, 0], D=17, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=13/15. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(No, -1/15)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (No, -1/15).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0090/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 91. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[15, 1, 2, 0], D=18, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=15/16. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(Yes, 0/1)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (Yes, 0/1).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0091/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 92. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[16, 1, 2, 0], D=19, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=17/17. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(No, 1/17)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (No, 1/17).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0092/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 93. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[17, 1, 2, 0], D=20, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=16/18. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(No, -1/18)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (No, -1/18).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0093/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 94. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[18, 1, 2, 0], D=21, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=18/19. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(Yes, 0/1)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (Yes, 0/1).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0094/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 95. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[19, 1, 2, 0], D=22, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=20/20. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(No, 1/20)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (No, 1/20).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0095/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 96. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[20, 1, 2, 0], D=23, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=19/21. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(No, -1/21)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (No, -1/21).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0096/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 97. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[21, 1, 2, 0], D=24, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=21/22. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(Yes, 0/1)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (Yes, 0/1).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0097/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 98. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[22, 1, 2, 0], D=25, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=23/23. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(No, 1/23)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (No, 1/23).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0098/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 99. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[23, 1, 2, 0], D=26, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=22/24. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(No, -1/24)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (No, -1/24).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0099/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate





## 100. Conditional Candidate Eligibility and Signed Defect

S={0,…,3}, F=P(S), masses=[24, 1, 2, 0], D=27, and w_i=mass_i/D. Masses are nonnegative and sum exactly to D; uniform weights are not assumed. A=[0, 2], B=[0, 1], P(B)>0. Candidate=24/25. Give (does it equal P(A|B)?, candidate−P(A|B)). A candidate outside [0,1] may be submitted for rejection.

View answer and explanation(Yes, 0/1)

Compute the actual conditional probability from the events, then subtract; only zero defect passes. An invalid probability candidate does not invalidate the underlying model. The exact result, retaining the requested order, is (Yes, 0/1).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261010-r04-conditional-probability-0100/)

Conditional probability in finite models · qf-density10-conditional-candidate-defect · candidate



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