task stringclasses 2
values | metadata dict | prompt stringlengths 486 4.05k | answer stringclasses 102
values |
|---|---|---|---|
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.6 and The probability of X_0 = 1 is 0.4.
The probability of X_1 = 0 is 0.43 and The probability of X_1 = 1 is 0.57.
The probability of X_2 = 0 is 0.57 and The probability of X_2 = 1 is 0.43.
Observed conditions:
Observing/Knowing that the state X_0 is equal to 0
Task: Compute p... | {0: 0.43, 1: 0.57} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.46 and The probability of X_0 = 1 is 0.54.
The probability of X_1 = 0 is 0.59 and The probability of X_1 = 1 is 0.41.
The probability of X_2 = 0 is 0.55 and The probability of X_2 = 1 is 0.45.
Observed conditions:
Doing/Imposing that the state X_2 is equal to 0
Task: Compute pr... | {0: 0.46, 1: 0.54} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_1 = 0 is 0.78 and The probability of X_1 = 1 is 0.22.
If X_1 = 0, then The probability of X_2 = 0 is 0.47 and The probability of X_2 = 1 is 0.53.
If X_1 = 1, then The probability of X_2 = 0 is 0.25 and The probability of X_2 = 1 is 0.75.
The probability of X_0 = 0 is 0.52 and The probabi... | {0: 0.47, 1: 0.53} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.49 and The probability of X_0 = 1 is 0.51.
If X_0 = 0, then The probability of X_1 = 0 is 0.46 and The probability of X_1 = 1 is 0.54.
If X_0 = 1, then The probability of X_1 = 0 is 0.67 and The probability of X_1 = 1 is 0.33.
The probability of X_2 = 0 is 0.07 and The probabi... | {0: 0.57, 1: 0.43} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.63 and The probability of X_0 = 1 is 0.37.
If X_0 = 0, then The probability of X_1 = 0 is 0.31 and The probability of X_1 = 1 is 0.69.
If X_0 = 1, then The probability of X_1 = 0 is 0.69 and The probability of X_1 = 1 is 0.31.
If X_0 = 0, then The probability of X_2 = 0 is 0.4... | {0: 0.53, 1: 0.47} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.82 and The probability of X_0 = 1 is 0.18.
If X_0 = 0, then The probability of X_2 = 0 is 0.3 and The probability of X_2 = 1 is 0.7.
If X_0 = 1, then The probability of X_2 = 0 is 0.78 and The probability of X_2 = 1 is 0.22.
The probability of X_1 = 0 is 0.77 and The probabili... | {0: 0.82, 1: 0.18} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.53 and The probability of X_0 = 1 is 0.47.
If X_0 = 0, then The probability of X_1 = 0 is 0.22 and The probability of X_1 = 1 is 0.78.
If X_0 = 1, then The probability of X_1 = 0 is 0.98 and The probability of X_1 = 1 is 0.02.
If X_0 = 0 and X_1 = 0, then The probability of X_... | {0: 0.2, 1: 0.8} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.72 and The probability of X_0 = 1 is 0.28.
If X_0 = 0, then The probability of X_1 = 0 is 0.97 and The probability of X_1 = 1 is 0.03.
If X_0 = 1, then The probability of X_1 = 0 is 0.2 and The probability of X_1 = 1 is 0.8.
If X_0 = 0 and X_1 = 0, then The probability of X_2 ... | {0: 0.97, 1: 0.03} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.34 and The probability of X_0 = 1 is 0.66.
If X_0 = 0, then The probability of X_1 = 0 is 0.33 and The probability of X_1 = 1 is 0.67.
If X_0 = 1, then The probability of X_1 = 0 is 0.54 and The probability of X_1 = 1 is 0.46.
The probability of X_2 = 0 is 0.31 and The probabi... | {0: 0.34, 1: 0.66} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.48 and The probability of X_0 = 1 is 0.52.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.55 and The probability of X_2 = 1 is 0.45.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.49 and The probability of X_2 = 1 is 0.51.
If X_0 = 1 and X_1 = 0, th... | {0: 0.43, 1: 0.57} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.35 and The probability of X_0 = 1 is 0.65.
If X_0 = 0, then The probability of X_1 = 0 is 0.52 and The probability of X_1 = 1 is 0.48.
If X_0 = 1, then The probability of X_1 = 0 is 0.22 and The probability of X_1 = 1 is 0.78.
If X_1 = 0, then The probability of X_2 = 0 is 0.4... | {0: 0.52, 1: 0.48} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.57 and The probability of X_0 = 1 is 0.43.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.79 and The probability of X_2 = 1 is 0.21.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.36 and The probability of X_2 = 1 is 0.64.
If X_0 = 1 and X_1 = 0, th... | {0: 0.32, 1: 0.68} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.57 and The probability of X_0 = 1 is 0.43.
If X_0 = 0, then The probability of X_1 = 0 is 0.67 and The probability of X_1 = 1 is 0.33.
If X_0 = 1, then The probability of X_1 = 0 is 0.27 and The probability of X_1 = 1 is 0.73.
If X_1 = 0, then The probability of X_2 = 0 is 0.4... | {0: 0.5, 1: 0.5} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.69 and The probability of X_0 = 1 is 0.31.
If X_0 = 0, then The probability of X_1 = 0 is 0.68 and The probability of X_1 = 1 is 0.32.
If X_0 = 1, then The probability of X_1 = 0 is 0.71 and The probability of X_1 = 1 is 0.29.
The probability of X_2 = 0 is 0.53 and The probabi... | {0: 0.53, 1: 0.47} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.69 and The probability of X_0 = 1 is 0.31.
If X_0 = 0, then The probability of X_1 = 0 is 0.14 and The probability of X_1 = 1 is 0.86.
If X_0 = 1, then The probability of X_1 = 0 is 0.62 and The probability of X_1 = 1 is 0.38.
If X_0 = 0 and X_1 = 0, then The probability of X_... | {0: 0.61, 1: 0.39} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.46 and The probability of X_0 = 1 is 0.54.
If X_0 = 0, then The probability of X_1 = 0 is 0.77 and The probability of X_1 = 1 is 0.23.
If X_0 = 1, then The probability of X_1 = 0 is 0.79 and The probability of X_1 = 1 is 0.21.
If X_0 = 0 and X_1 = 0, then The probability of X_... | {0: 0.68, 1: 0.32} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.72 and The probability of X_0 = 1 is 0.28.
If X_0 = 0, then The probability of X_1 = 0 is 0.23 and The probability of X_1 = 1 is 0.77.
If X_0 = 1, then The probability of X_1 = 0 is 0.68 and The probability of X_1 = 1 is 0.32.
The probability of X_2 = 0 is 0.51 and The probabi... | {0: 0.86, 1: 0.14} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.07 and The probability of X_0 = 1 is 0.93.
If X_0 = 0, then The probability of X_1 = 0 is 0.02 and The probability of X_1 = 1 is 0.98.
If X_0 = 1, then The probability of X_1 = 0 is 0.32 and The probability of X_1 = 1 is 0.68.
If X_1 = 0, then The probability of X_2 = 0 is 0.8... | {0: 0.76, 1: 0.24} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.82 and The probability of X_0 = 1 is 0.18.
If X_0 = 0, then The probability of X_1 = 0 is 0.13 and The probability of X_1 = 1 is 0.87.
If X_0 = 1, then The probability of X_1 = 0 is 0.62 and The probability of X_1 = 1 is 0.38.
If X_0 = 0 and X_1 = 0, then The probability of X_... | {0: 0.35, 1: 0.65} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.68 and The probability of X_0 = 1 is 0.32.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.21 and The probability of X_2 = 1 is 0.79.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.58 and The probability of X_2 = 1 is 0.42.
If X_0 = 1 and X_1 = 0, th... | {0: 0.81, 1: 0.19} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.51 and The probability of X_0 = 1 is 0.49.
If X_0 = 0, then The probability of X_1 = 0 is 0.52 and The probability of X_1 = 1 is 0.48.
If X_0 = 1, then The probability of X_1 = 0 is 0.07 and The probability of X_1 = 1 is 0.93.
If X_1 = 0, then The probability of X_2 = 0 is 0.3... | {0: 0.46, 1: 0.54} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.66 and The probability of X_0 = 1 is 0.34.
If X_0 = 0, then The probability of X_1 = 0 is 0.52 and The probability of X_1 = 1 is 0.48.
If X_0 = 1, then The probability of X_1 = 0 is 0.78 and The probability of X_1 = 1 is 0.22.
The probability of X_2 = 0 is 0.83 and The probabi... | {0: 0.78, 1: 0.22} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.99 and The probability of X_0 = 1 is 0.01.
If X_0 = 0, then The probability of X_1 = 0 is 0.54 and The probability of X_1 = 1 is 0.46.
If X_0 = 1, then The probability of X_1 = 0 is 0.51 and The probability of X_1 = 1 is 0.49.
If X_1 = 0, then The probability of X_2 = 0 is 0.7... | {0: 0.57, 1: 0.43} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.75 and The probability of X_0 = 1 is 0.25.
If X_0 = 0, then The probability of X_1 = 0 is 0.69 and The probability of X_1 = 1 is 0.31.
If X_0 = 1, then The probability of X_1 = 0 is 0.63 and The probability of X_1 = 1 is 0.37.
If X_0 = 0, then The probability of X_2 = 0 is 0.5... | {0: 0.63, 1: 0.37} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_1 = 0 is 0.66 and The probability of X_1 = 1 is 0.34.
If X_1 = 0, then The probability of X_2 = 0 is 0.52 and The probability of X_2 = 1 is 0.48.
If X_1 = 1, then The probability of X_2 = 0 is 0.24 and The probability of X_2 = 1 is 0.76.
The probability of X_0 = 0 is 0.55 and The probabi... | {0: 0.66, 1: 0.34} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.44 and The probability of X_0 = 1 is 0.56.
The probability of X_1 = 0 is 0.4 and The probability of X_1 = 1 is 0.6.
The probability of X_2 = 0 is 0.32 and The probability of X_2 = 1 is 0.68.
Observed conditions:
Doing/Imposing that the state X_2 is equal to 0
Task: Compute prob... | {0: 0.44, 1: 0.56} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.58 and The probability of X_0 = 1 is 0.42.
If X_0 = 0, then The probability of X_1 = 0 is 0.52 and The probability of X_1 = 1 is 0.48.
If X_0 = 1, then The probability of X_1 = 0 is 0.5 and The probability of X_1 = 1 is 0.5.
If X_0 = 0, then The probability of X_2 = 0 is 0.86 ... | {0: 0.5, 1: 0.5} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.64 and The probability of X_0 = 1 is 0.36.
If X_0 = 0, then The probability of X_1 = 0 is 0.47 and The probability of X_1 = 1 is 0.53.
If X_0 = 1, then The probability of X_1 = 0 is 0.77 and The probability of X_1 = 1 is 0.23.
The probability of X_2 = 0 is 0.79 and The probabi... | {0: 0.79, 1: 0.21} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.15 and The probability of X_0 = 1 is 0.85.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.67 and The probability of X_2 = 1 is 0.33.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.39 and The probability of X_2 = 1 is 0.61.
If X_0 = 1 and X_1 = 0, th... | {0: 0.36, 1: 0.64} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.5 and The probability of X_0 = 1 is 0.5.
The probability of X_1 = 0 is 0.55 and The probability of X_1 = 1 is 0.45.
The probability of X_2 = 0 is 0.93 and The probability of X_2 = 1 is 0.07.
Observed conditions:
Doing/Imposing that the state X_2 is equal to 0
Task: Compute prob... | {0: 0.55, 1: 0.45} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.47 and The probability of X_0 = 1 is 0.53.
The probability of X_1 = 0 is 0.42 and The probability of X_1 = 1 is 0.58.
The probability of X_2 = 0 is 0.38 and The probability of X_2 = 1 is 0.62.
Observed conditions:
Observing/Knowing that the state X_0 is equal to 0, and the stat... | {0: 0.38, 1: 0.62} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.44 and The probability of X_0 = 1 is 0.56.
If X_0 = 0, then The probability of X_1 = 0 is 0.7 and The probability of X_1 = 1 is 0.3.
If X_0 = 1, then The probability of X_1 = 0 is 0.82 and The probability of X_1 = 1 is 0.18.
If X_0 = 0, then The probability of X_2 = 0 is 0.47 ... | {0: 0.77, 1: 0.23} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.53 and The probability of X_0 = 1 is 0.47.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.17 and The probability of X_2 = 1 is 0.83.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.53 and The probability of X_2 = 1 is 0.47.
If X_0 = 1 and X_1 = 0, th... | {0: 0.53, 1: 0.47} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.42 and The probability of X_0 = 1 is 0.58.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.23 and The probability of X_2 = 1 is 0.77.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.02 and The probability of X_2 = 1 is 0.98.
If X_0 = 1 and X_1 = 0, th... | {0: 0.73, 1: 0.27} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.19 and The probability of X_0 = 1 is 0.81.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.45 and The probability of X_2 = 1 is 0.55.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.08 and The probability of X_2 = 1 is 0.92.
If X_0 = 1 and X_1 = 0, th... | {0: 0.47, 1: 0.53} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.45 and The probability of X_0 = 1 is 0.55.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.17 and The probability of X_2 = 1 is 0.83.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.99 and The probability of X_2 = 1 is 0.01.
If X_0 = 1 and X_1 = 0, th... | {0: 0.45, 1: 0.55} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.71 and The probability of X_0 = 1 is 0.29.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.96 and The probability of X_2 = 1 is 0.04.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.02 and The probability of X_2 = 1 is 0.98.
If X_0 = 1 and X_1 = 0, th... | {0: 0.71, 1: 0.29} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.63 and The probability of X_0 = 1 is 0.37.
If X_0 = 0, then The probability of X_1 = 0 is 0.19 and The probability of X_1 = 1 is 0.81.
If X_0 = 1, then The probability of X_1 = 0 is 0.89 and The probability of X_1 = 1 is 0.11.
If X_0 = 0 and X_1 = 0, then The probability of X_... | {0: 0.63, 1: 0.37} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.83 and The probability of X_0 = 1 is 0.17.
If X_0 = 0, then The probability of X_1 = 0 is 0.01 and The probability of X_1 = 1 is 0.99.
If X_0 = 1, then The probability of X_1 = 0 is 0.47 and The probability of X_1 = 1 is 0.53.
If X_0 = 0, then The probability of X_2 = 0 is 0.4... | {0: 0.69, 1: 0.31} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.6 and The probability of X_0 = 1 is 0.4.
If X_0 = 0, then The probability of X_1 = 0 is 0.37 and The probability of X_1 = 1 is 0.63.
If X_0 = 1, then The probability of X_1 = 0 is 0.41 and The probability of X_1 = 1 is 0.59.
If X_0 = 0, then The probability of X_2 = 0 is 0.93 ... | {0: 0.62, 1: 0.38} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.81 and The probability of X_0 = 1 is 0.19.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.39 and The probability of X_2 = 1 is 0.61.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.44 and The probability of X_2 = 1 is 0.56.
If X_0 = 1 and X_1 = 0, th... | {0: 0.24, 1: 0.76} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.68 and The probability of X_0 = 1 is 0.32.
If X_0 = 0, then The probability of X_2 = 0 is 0.73 and The probability of X_2 = 1 is 0.27.
If X_0 = 1, then The probability of X_2 = 0 is 0.47 and The probability of X_2 = 1 is 0.53.
The probability of X_1 = 0 is 0.24 and The probabi... | {0: 0.68, 1: 0.32} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.6 and The probability of X_0 = 1 is 0.4.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.79 and The probability of X_2 = 1 is 0.21.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.32 and The probability of X_2 = 1 is 0.68.
If X_0 = 1 and X_1 = 0, then... | {0: 0.58, 1: 0.42} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.26 and The probability of X_0 = 1 is 0.74.
If X_0 = 0, then The probability of X_1 = 0 is 0.51 and The probability of X_1 = 1 is 0.49.
If X_0 = 1, then The probability of X_1 = 0 is 0.65 and The probability of X_1 = 1 is 0.35.
If X_0 = 0 and X_1 = 0, then The probability of X_... | {0: 0.65, 1: 0.35} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_1 = 0 is 0.52 and The probability of X_1 = 1 is 0.48.
If X_1 = 0, then The probability of X_2 = 0 is 0.35 and The probability of X_2 = 1 is 0.65.
If X_1 = 1, then The probability of X_2 = 0 is 0.33 and The probability of X_2 = 1 is 0.67.
The probability of X_0 = 0 is 0.71 and The probabi... | {0: 0.71, 1: 0.29} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.54 and The probability of X_0 = 1 is 0.46.
If X_0 = 0, then The probability of X_1 = 0 is 0.67 and The probability of X_1 = 1 is 0.33.
If X_0 = 1, then The probability of X_1 = 0 is 0.18 and The probability of X_1 = 1 is 0.82.
If X_0 = 0 and X_1 = 0, then The probability of X_... | {0: 0.6, 1: 0.4} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.27 and The probability of X_0 = 1 is 0.73.
If X_0 = 0, then The probability of X_2 = 0 is 0.09 and The probability of X_2 = 1 is 0.91.
If X_0 = 1, then The probability of X_2 = 0 is 0.17 and The probability of X_2 = 1 is 0.83.
The probability of X_1 = 0 is 0.64 and The probabi... | {0: 0.64, 1: 0.36} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.75 and The probability of X_0 = 1 is 0.25.
If X_0 = 0, then The probability of X_1 = 0 is 0.1 and The probability of X_1 = 1 is 0.9.
If X_0 = 1, then The probability of X_1 = 0 is 0.35 and The probability of X_1 = 1 is 0.65.
If X_0 = 0, then The probability of X_2 = 0 is 0.8 a... | {0: 0.1, 1: 0.9} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.56 and The probability of X_0 = 1 is 0.44.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.72 and The probability of X_2 = 1 is 0.28.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.36 and The probability of X_2 = 1 is 0.64.
If X_0 = 1 and X_1 = 0, th... | {0: 0.82, 1: 0.18} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.45 and The probability of X_0 = 1 is 0.55.
If X_0 = 0, then The probability of X_1 = 0 is 0.22 and The probability of X_1 = 1 is 0.78.
If X_0 = 1, then The probability of X_1 = 0 is 0.31 and The probability of X_1 = 1 is 0.69.
If X_1 = 0, then The probability of X_2 = 0 is 0.4... | {0: 0.22, 1: 0.78} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.3 and The probability of X_0 = 1 is 0.7.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.19 and The probability of X_2 = 1 is 0.81.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.57 and The probability of X_2 = 1 is 0.43.
If X_0 = 1 and X_1 = 0, then... | {0: 0.51, 1: 0.49} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.16 and The probability of X_0 = 1 is 0.84.
If X_0 = 0, then The probability of X_1 = 0 is 0.24 and The probability of X_1 = 1 is 0.76.
If X_0 = 1, then The probability of X_1 = 0 is 0.83 and The probability of X_1 = 1 is 0.17.
If X_1 = 0, then The probability of X_2 = 0 is 0.6... | {0: 0.46, 1: 0.54} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.16 and The probability of X_0 = 1 is 0.84.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.29 and The probability of X_2 = 1 is 0.71.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.74 and The probability of X_2 = 1 is 0.26.
If X_0 = 1 and X_1 = 0, th... | {0: 0.49, 1: 0.51} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.6 and The probability of X_0 = 1 is 0.4.
If X_0 = 0, then The probability of X_1 = 0 is 0.31 and The probability of X_1 = 1 is 0.69.
If X_0 = 1, then The probability of X_1 = 0 is 0.15 and The probability of X_1 = 1 is 0.85.
If X_0 = 0 and X_1 = 0, then The probability of X_2 ... | {0: 0.13, 1: 0.87} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.73 and The probability of X_0 = 1 is 0.27.
If X_0 = 0, then The probability of X_1 = 0 is 0.67 and The probability of X_1 = 1 is 0.33.
If X_0 = 1, then The probability of X_1 = 0 is 0.51 and The probability of X_1 = 1 is 0.49.
If X_0 = 0, then The probability of X_2 = 0 is 0.3... | {0: 0.63, 1: 0.37} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.5 and The probability of X_0 = 1 is 0.5.
If X_0 = 0, then The probability of X_1 = 0 is 0.58 and The probability of X_1 = 1 is 0.42.
If X_0 = 1, then The probability of X_1 = 0 is 0.59 and The probability of X_1 = 1 is 0.41.
If X_1 = 0, then The probability of X_2 = 0 is 0.43 ... | {0: 0.5, 1: 0.5} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_1 = 0 is 0.33 and The probability of X_1 = 1 is 0.67.
If X_1 = 0, then The probability of X_2 = 0 is 0.57 and The probability of X_2 = 1 is 0.43.
If X_1 = 1, then The probability of X_2 = 0 is 0.55 and The probability of X_2 = 1 is 0.45.
The probability of X_0 = 0 is 0.52 and The probabi... | {0: 0.56, 1: 0.44} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.63 and The probability of X_0 = 1 is 0.37.
If X_0 = 0, then The probability of X_1 = 0 is 0.54 and The probability of X_1 = 1 is 0.46.
If X_0 = 1, then The probability of X_1 = 0 is 0.63 and The probability of X_1 = 1 is 0.37.
If X_0 = 0 and X_1 = 0, then The probability of X_... | {0: 0.63, 1: 0.37} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.48 and The probability of X_0 = 1 is 0.52.
If X_0 = 0, then The probability of X_1 = 0 is 0.38 and The probability of X_1 = 1 is 0.62.
If X_0 = 1, then The probability of X_1 = 0 is 0.19 and The probability of X_1 = 1 is 0.81.
If X_1 = 0, then The probability of X_2 = 0 is 0.3... | {0: 0.45, 1: 0.55} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.26 and The probability of X_0 = 1 is 0.74.
If X_0 = 0, then The probability of X_1 = 0 is 0.23 and The probability of X_1 = 1 is 0.77.
If X_0 = 1, then The probability of X_1 = 0 is 0.46 and The probability of X_1 = 1 is 0.54.
If X_0 = 0 and X_1 = 0, then The probability of X_... | {0: 0.34, 1: 0.66} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.49 and The probability of X_0 = 1 is 0.51.
If X_0 = 0, then The probability of X_2 = 0 is 0.59 and The probability of X_2 = 1 is 0.41.
If X_0 = 1, then The probability of X_2 = 0 is 0.58 and The probability of X_2 = 1 is 0.42.
The probability of X_1 = 0 is 0.16 and The probabi... | {0: 0.49, 1: 0.51} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.27 and The probability of X_0 = 1 is 0.73.
If X_0 = 0, then The probability of X_1 = 0 is 0.5 and The probability of X_1 = 1 is 0.5.
If X_0 = 1, then The probability of X_1 = 0 is 0.27 and The probability of X_1 = 1 is 0.73.
If X_0 = 0, then The probability of X_2 = 0 is 0.26 ... | {0: 0.27, 1: 0.73} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_1 = 0 is 0.0 and The probability of X_1 = 1 is 1.0.
If X_1 = 0, then The probability of X_2 = 0 is 0.44 and The probability of X_2 = 1 is 0.56.
If X_1 = 1, then The probability of X_2 = 0 is 0.96 and The probability of X_2 = 1 is 0.04.
The probability of X_0 = 0 is 0.4 and The probabilit... | {0: 0.0, 1: 1.0} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.67 and The probability of X_0 = 1 is 0.33.
If X_0 = 0, then The probability of X_1 = 0 is 0.92 and The probability of X_1 = 1 is 0.08.
If X_0 = 1, then The probability of X_1 = 0 is 0.79 and The probability of X_1 = 1 is 0.21.
If X_0 = 0 and X_1 = 0, then The probability of X_... | {0: 0.85, 1: 0.15} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.24 and The probability of X_0 = 1 is 0.76.
If X_0 = 0, then The probability of X_1 = 0 is 0.62 and The probability of X_1 = 1 is 0.38.
If X_0 = 1, then The probability of X_1 = 0 is 0.15 and The probability of X_1 = 1 is 0.85.
If X_0 = 0 and X_1 = 0, then The probability of X_... | {0: 0.5, 1: 0.5} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.86 and The probability of X_0 = 1 is 0.14.
If X_0 = 0, then The probability of X_1 = 0 is 0.91 and The probability of X_1 = 1 is 0.09.
If X_0 = 1, then The probability of X_1 = 0 is 0.33 and The probability of X_1 = 1 is 0.67.
If X_0 = 0 and X_1 = 0, then The probability of X_... | {0: 0.86, 1: 0.14} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.64 and The probability of X_0 = 1 is 0.36.
If X_0 = 0, then The probability of X_1 = 0 is 0.65 and The probability of X_1 = 1 is 0.35.
If X_0 = 1, then The probability of X_1 = 0 is 0.31 and The probability of X_1 = 1 is 0.69.
If X_1 = 0, then The probability of X_2 = 0 is 0.7... | {0: 0.64, 1: 0.36} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.66 and The probability of X_0 = 1 is 0.34.
If X_0 = 0, then The probability of X_1 = 0 is 0.87 and The probability of X_1 = 1 is 0.13.
If X_0 = 1, then The probability of X_1 = 0 is 0.31 and The probability of X_1 = 1 is 0.69.
The probability of X_2 = 0 is 0.06 and The probabi... | {0: 0.68, 1: 0.32} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.67 and The probability of X_0 = 1 is 0.33.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.56 and The probability of X_2 = 1 is 0.44.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.89 and The probability of X_2 = 1 is 0.11.
If X_0 = 1 and X_1 = 0, th... | {0: 0.23, 1: 0.77} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.67 and The probability of X_0 = 1 is 0.33.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.27 and The probability of X_2 = 1 is 0.73.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.29 and The probability of X_2 = 1 is 0.71.
If X_0 = 1 and X_1 = 0, th... | {0: 0.27, 1: 0.73} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.49 and The probability of X_0 = 1 is 0.51.
If X_0 = 0, then The probability of X_2 = 0 is 0.46 and The probability of X_2 = 1 is 0.54.
If X_0 = 1, then The probability of X_2 = 0 is 0.9 and The probability of X_2 = 1 is 0.1.
The probability of X_1 = 0 is 0.32 and The probabili... | {0: 0.32, 1: 0.68} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.58 and The probability of X_0 = 1 is 0.42.
If X_0 = 0, then The probability of X_1 = 0 is 0.13 and The probability of X_1 = 1 is 0.87.
If X_0 = 1, then The probability of X_1 = 0 is 0.38 and The probability of X_1 = 1 is 0.62.
If X_0 = 0 and X_1 = 0, then The probability of X_... | {0: 0.85, 1: 0.15} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.51 and The probability of X_0 = 1 is 0.49.
If X_0 = 0, then The probability of X_1 = 0 is 0.9 and The probability of X_1 = 1 is 0.1.
If X_0 = 1, then The probability of X_1 = 0 is 0.76 and The probability of X_1 = 1 is 0.24.
The probability of X_2 = 0 is 0.78 and The probabili... | {0: 0.78, 1: 0.22} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.46 and The probability of X_0 = 1 is 0.54.
If X_0 = 0, then The probability of X_1 = 0 is 0.91 and The probability of X_1 = 1 is 0.09.
If X_0 = 1, then The probability of X_1 = 0 is 0.22 and The probability of X_1 = 1 is 0.78.
If X_0 = 0, then The probability of X_2 = 0 is 0.6... | {0: 0.54, 1: 0.46} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.51 and The probability of X_0 = 1 is 0.49.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.49 and The probability of X_2 = 1 is 0.51.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.63 and The probability of X_2 = 1 is 0.37.
If X_0 = 1 and X_1 = 0, th... | {0: 0.35, 1: 0.65} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.45 and The probability of X_0 = 1 is 0.55.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.98 and The probability of X_2 = 1 is 0.02.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.15 and The probability of X_2 = 1 is 0.85.
If X_0 = 1 and X_1 = 0, th... | {0: 0.45, 1: 0.55} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.52 and The probability of X_0 = 1 is 0.48.
If X_0 = 0 and X_1 = 0, then The probability of X_2 = 0 is 0.53 and The probability of X_2 = 1 is 0.47.
If X_0 = 0 and X_1 = 1, then The probability of X_2 = 0 is 0.57 and The probability of X_2 = 1 is 0.43.
If X_0 = 1 and X_1 = 0, th... | {0: 0.68, 1: 0.32} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.57 and The probability of X_0 = 1 is 0.43.
If X_0 = 0, then The probability of X_1 = 0 is 0.84 and The probability of X_1 = 1 is 0.16.
If X_0 = 1, then The probability of X_1 = 0 is 0.46 and The probability of X_1 = 1 is 0.54.
If X_0 = 0 and X_1 = 0, then The probability of X_... | {0: 0.68, 1: 0.32} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.51 and The probability of X_0 = 1 is 0.49.
If X_0 = 0, then The probability of X_1 = 0 is 0.42 and The probability of X_1 = 1 is 0.58.
If X_0 = 1, then The probability of X_1 = 0 is 0.63 and The probability of X_1 = 1 is 0.37.
If X_1 = 0, then The probability of X_2 = 0 is 0.3... | {0: 0.82, 1: 0.18} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.11 and The probability of X_0 = 1 is 0.89.
If X_0 = 0, then The probability of X_1 = 0 is 0.62 and The probability of X_1 = 1 is 0.38.
If X_0 = 1, then The probability of X_1 = 0 is 0.86 and The probability of X_1 = 1 is 0.14.
If X_0 = 0, then The probability of X_2 = 0 is 0.5... | {0: 0.46, 1: 0.54} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.8,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.9 and The probability of X_0 = 1 is 0.1.
If X_0 = 0, then The probability of X_1 = 0 is 0.49 and The probability of X_1 = 1 is 0.51.
If X_0 = 1, then The probability of X_1 = 0 is 0.11 and The probability of X_1 = 1 is 0.89.
If X_0 = 0 and X_1 = 0, then The probability of X_2 ... | {0: 0.88, 1: 0.12} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.8,
"graph_generation_mode": "erdos",
"is_verbose": true,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": nul... | System:
The probability of X_0 = 0 is 0.43 and The probability of X_0 = 1 is 0.57.
If X_0 = 0, then The probability of X_1 = 0 is 0.63 and The probability of X_1 = 1 is 0.37.
If X_0 = 1, then The probability of X_1 = 0 is 0.37 and The probability of X_1 = 1 is 0.63.
If X_1 = 0, then The probability of X_2 = 0 is 0.3... | {0: 0.31, 1: 0.69} |
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