Question bank

test intercity-probability-v2-5

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 45 thousand dollars. air: cost 60 dollars; waiting 64 min; in-vehicle 144 min; generalized cost 82 dollars. train: cost 32 dollars; waiting 44 min; in-vehicle 404 min; generalized cost 93 dollars. bus: cost 26 dollars; waiting 53 min; in-vehicle 449 min; generalized cost 94 dollars. car: cost 8 dollars; waiting 0 min; in-vehicle 600 min; generalized cost 99 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.32, "train": 0.28, "bus": 0.22, "car": 0.18}	error 0.902
Llama 3.3	{"air": 0.43, "train": 0.26, "bus": 0.15, "car": 0.16}	error 0.981
Qwen · off	{"air": 0.38, "train": 0.28, "bus": 0.22, "car": 0.12}	error 1.05
Qwen · on	{"air": 0.35, "train": 0.25, "bus": 0.22, "car": 0.18}	error 0.906

test intercity-probability-v2-6

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 20 thousand dollars. air: cost 59 dollars; waiting 69 min; in-vehicle 100 min; generalized cost 70 dollars. train: cost 20 dollars; waiting 40 min; in-vehicle 345 min; generalized cost 57 dollars. bus: cost 13 dollars; waiting 35 min; in-vehicle 417 min; generalized cost 58 dollars. car: cost 12 dollars; waiting 0 min; in-vehicle 284 min; generalized cost 43 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.05, "train": 0.25, "bus": 0.2, "car": 0.5}	error 0.855
Llama 3.3	{"air": 0.05, "train": 0.15, "bus": 0.1, "car": 0.7}	error 1.22
Qwen · off	{"air": 0.05, "train": 0.25, "bus": 0.2, "car": 0.5}	error 0.855
Qwen · on	{"air": 0.14, "train": 0.23, "bus": 0.22, "car": 0.41}	error 0.829

test intercity-probability-v2-17

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 26 thousand dollars. air: cost 61 dollars; waiting 69 min; in-vehicle 74 min; generalized cost 69 dollars. train: cost 38 dollars; waiting 15 min; in-vehicle 255 min; generalized cost 66 dollars. bus: cost 26 dollars; waiting 35 min; in-vehicle 389 min; generalized cost 68 dollars. car: cost 13 dollars; waiting 0 min; in-vehicle 315 min; generalized cost 47 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.12, "train": 0.28, "bus": 0.25, "car": 0.35}	error 0.718
Llama 3.3	{"air": 0.35, "train": 0.25, "bus": 0.1, "car": 0.3}	error 0.785
Qwen · off	{"air": 0.24, "train": 0.25, "bus": 0.24, "car": 0.27}	error 0.751
Qwen · on	{"air": 0.207, "train": 0.223, "bus": 0.212, "car": 0.358}	error 0.82

test intercity-probability-v2-20

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 72 thousand dollars. air: cost 58 dollars; waiting 64 min; in-vehicle 93 min; generalized cost 72 dollars. train: cost 28 dollars; waiting 10 min; in-vehicle 305 min; generalized cost 75 dollars. bus: cost 25 dollars; waiting 53 min; in-vehicle 346 min; generalized cost 78 dollars. car: cost 9 dollars; waiting 0 min; in-vehicle 316 min; generalized cost 57 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.28, "train": 0.26, "bus": 0.22, "car": 0.24}	error 0.732
Llama 3.3	{"air": 0.417, "train": 0.208, "bus": 0.146, "car": 0.229}	error 0.875
Qwen · off	{"air": 0.15, "train": 0.12, "bus": 0.08, "car": 0.65}	error 1.23
Qwen · on	{"air": 0.21, "train": 0.18, "bus": 0.16, "car": 0.45}	error 0.945

test intercity-probability-v2-26

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 60 thousand dollars. air: cost 85 dollars; waiting 30 min; in-vehicle 140 min; generalized cost 106 dollars. train: cost 90 dollars; waiting 44 min; in-vehicle 928 min; generalized cost 231 dollars. bus: cost 45 dollars; waiting 53 min; in-vehicle 918 min; generalized cost 185 dollars. car: cost 86 dollars; waiting 0 min; in-vehicle 902 min; generalized cost 223 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.58, "train": 0.08, "bus": 0.12, "car": 0.22}	error 0.246
Llama 3.3	{"air": 0.513, "train": 0.063, "bus": 0.191, "car": 0.233}	error 0.332
Qwen · off	{"air": 0.62, "train": 0.05, "bus": 0.18, "car": 0.15}	error 0.202
Qwen · on	{"air": 0.613, "train": 0.094, "bus": 0.187, "car": 0.106}	error 0.205

test intercity-probability-v2-30

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 6 thousand dollars. air: cost 59 dollars; waiting 69 min; in-vehicle 100 min; generalized cost 70 dollars. train: cost 11 dollars; waiting 2 min; in-vehicle 285 min; generalized cost 42 dollars. bus: cost 13 dollars; waiting 35 min; in-vehicle 417 min; generalized cost 58 dollars. car: cost 13 dollars; waiting 0 min; in-vehicle 284 min; generalized cost 44 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.05, "train": 0.45, "bus": 0.15, "car": 0.35}	error 0.45
Llama 3.3	{"air": 0.05, "train": 0.4, "bus": 0.1, "car": 0.45}	error 0.575
Qwen · off	{"air": 0.05, "train": 0.45, "bus": 0.15, "car": 0.35}	error 0.45
Qwen · on	{"air": 0.16, "train": 0.32, "bus": 0.21, "car": 0.31}	error 0.628

test intercity-probability-v2-41

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 26 thousand dollars. air: cost 125 dollars; waiting 75 min; in-vehicle 110 min; generalized cost 137 dollars. train: cost 70 dollars; waiting 34 min; in-vehicle 596 min; generalized cost 135 dollars. bus: cost 31 dollars; waiting 35 min; in-vehicle 590 min; generalized cost 95 dollars. car: cost 24 dollars; waiting 0 min; in-vehicle 577 min; generalized cost 87 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.12, "train": 0.13, "bus": 0.35, "car": 0.4}	error 1.07
Llama 3.3	{"air": 0.05, "train": 0.15, "bus": 0.2, "car": 0.6}	error 1.32
Qwen · off	{"air": 0.25, "train": 0.25, "bus": 0.25, "car": 0.25}	error 0.75
Qwen · on	{"air": 0.12, "train": 0.13, "bus": 0.34, "car": 0.42}	error 1.08

test intercity-probability-v2-45

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 8 thousand dollars. air: cost 105 dollars; waiting 45 min; in-vehicle 115 min; generalized cost 122 dollars. train: cost 35 dollars; waiting 44 min; in-vehicle 622 min; generalized cost 130 dollars. bus: cost 31 dollars; waiting 53 min; in-vehicle 616 min; generalized cost 125 dollars. car: cost 12 dollars; waiting 0 min; in-vehicle 577 min; generalized cost 100 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.32, "train": 0.22, "bus": 0.24, "car": 0.22}	error 0.617
Llama 3.3	{"air": 0.35, "train": 0.15, "bus": 0.2, "car": 0.3}	error 0.575
Qwen · off	{"air": 0.24, "train": 0.22, "bus": 0.23, "car": 0.31}	error 0.775
Qwen · on	{"air": 0.18, "train": 0.13, "bus": 0.19, "car": 0.5}	error 0.975

test intercity-probability-v2-46

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 70 thousand dollars. air: cost 106 dollars; waiting 20 min; in-vehicle 190 min; generalized cost 127 dollars. train: cost 72 dollars; waiting 34 min; in-vehicle 659 min; generalized cost 143 dollars. bus: cost 33 dollars; waiting 35 min; in-vehicle 653 min; generalized cost 104 dollars. car: cost 44 dollars; waiting 0 min; in-vehicle 592 min; generalized cost 108 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.28, "train": 0.18, "bus": 0.27, "car": 0.27}	error 0.697
Llama 3.3	{"air": 0.35, "train": 0.15, "bus": 0.25, "car": 0.25}	error 0.57
Qwen · off	{"air": 0.05, "train": 0.08, "bus": 0.42, "car": 0.45}	error 1.29
Qwen · on	{"air": 0.2315, "train": 0.1973, "bus": 0.2913, "car": 0.2799}	error 0.793

test intercity-probability-v2-55

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 6 thousand dollars. air: cost 45 dollars; waiting 64 min; in-vehicle 73 min; generalized cost 56 dollars. train: cost 22 dollars; waiting 15 min; in-vehicle 290 min; generalized cost 66 dollars. bus: cost 13 dollars; waiting 53 min; in-vehicle 395 min; generalized cost 73 dollars. car: cost 5 dollars; waiting 0 min; in-vehicle 314 min; generalized cost 53 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.28, "train": 0.24, "bus": 0.15, "car": 0.33}	error 0.787
Llama 3.3	{"air": 0.35, "train": 0.25, "bus": 0.1, "car": 0.3}	error 0.785
Qwen · off	{"air": 0.18, "train": 0.12, "bus": 0.08, "car": 0.62}	error 1.2
Qwen · on	{"air": 0.345, "train": 0.127, "bus": 0.063, "car": 0.465}	error 1.1

test intercity-probability-v2-64

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 6 thousand dollars. air: cost 103 dollars; waiting 69 min; in-vehicle 138 min; generalized cost 118 dollars. train: cost 22 dollars; waiting 5 min; in-vehicle 800 min; generalized cost 109 dollars. bus: cost 43 dollars; waiting 35 min; in-vehicle 821 min; generalized cost 132 dollars. car: cost 36 dollars; waiting 0 min; in-vehicle 846 min; generalized cost 128 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.24, "train": 0.32, "bus": 0.18, "car": 0.26}	error 0.62
Llama 3.3	{"air": 0.231, "train": 0.308, "bus": 0.154, "car": 0.307}	error 0.65
Qwen · off	{"air": 0.25, "train": 0.45, "bus": 0.15, "car": 0.15}	error 0.41
Qwen · on	{"air": 0.27, "train": 0.34, "bus": 0.19, "car": 0.2}	error 0.585

test intercity-probability-v2-74

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 15 thousand dollars. air: cost 104 dollars; waiting 69 min; in-vehicle 200 min; generalized cost 126 dollars. train: cost 23 dollars; waiting 75 min; in-vehicle 835 min; generalized cost 114 dollars. bus: cost 43 dollars; waiting 35 min; in-vehicle 846 min; generalized cost 135 dollars. car: cost 40 dollars; waiting 0 min; in-vehicle 927 min; generalized cost 141 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.28, "train": 0.32, "bus": 0.2, "car": 0.2}	error 0.621
Llama 3.3	{"air": 0.403, "train": 0.297, "bus": 0.194, "car": 0.106}	error 0.705
Qwen · off	{"air": 0.25, "train": 0.45, "bus": 0.15, "car": 0.15}	error 0.41
Qwen · on	{"air": 0.259, "train": 0.418, "bus": 0.181, "car": 0.142}	error 0.459

test intercity-probability-v2-77

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 30 thousand dollars. air: cost 103 dollars; waiting 69 min; in-vehicle 125 min; generalized cost 116 dollars. train: cost 80 dollars; waiting 30 min; in-vehicle 800 min; generalized cost 167 dollars. bus: cost 42 dollars; waiting 35 min; in-vehicle 844 min; generalized cost 134 dollars. car: cost 38 dollars; waiting 0 min; in-vehicle 861 min; generalized cost 132 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.32, "train": 0.18, "bus": 0.22, "car": 0.28}	error 0.902
Llama 3.3	{"air": 0.35, "train": 0.05, "bus": 0.1, "car": 0.5}	error 1.28
Qwen · off	{"air": 0.05, "train": 0.02, "bus": 0.46, "car": 0.47}	error 1.4
Qwen · on	{"air": 0.33, "train": 0.15, "bus": 0.26, "car": 0.26}	error 0.967

test intercity-probability-v2-92

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 12 thousand dollars. air: cost 58 dollars; waiting 69 min; in-vehicle 124 min; generalized cost 71 dollars. train: cost 30 dollars; waiting 10 min; in-vehicle 340 min; generalized cost 67 dollars. bus: cost 25 dollars; waiting 35 min; in-vehicle 427 min; generalized cost 71 dollars. car: cost 14 dollars; waiting 0 min; in-vehicle 364 min; generalized cost 54 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.12, "train": 0.35, "bus": 0.18, "car": 0.35}	error 0.592
Llama 3.3	{"air": 0.15, "train": 0.25, "bus": 0.1, "car": 0.5}	error 0.845
Qwen · off	{"air": 0.15, "train": 0.25, "bus": 0.15, "car": 0.45}	error 0.81
Qwen · on	{"air": 0.17, "train": 0.22, "bus": 0.17, "car": 0.44}	error 0.86

test intercity-probability-v2-93

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 70 thousand dollars. air: cost 84 dollars; waiting 64 min; in-vehicle 108 min; generalized cost 100 dollars. train: cost 70 dollars; waiting 44 min; in-vehicle 596 min; generalized cost 160 dollars. bus: cost 31 dollars; waiting 53 min; in-vehicle 590 min; generalized cost 120 dollars. car: cost 15 dollars; waiting 0 min; in-vehicle 360 min; generalized cost 70 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.32, "train": 0.12, "bus": 0.14, "car": 0.42}	error 0.473
Llama 3.3	{"air": 0.4, "train": 0.1, "bus": 0.2, "car": 0.3}	error 0.7
Qwen · off	{"air": 0.05, "train": 0.05, "bus": 0.15, "car": 0.75}	error 0.09
Qwen · on	{"air": 0.27, "train": 0.13, "bus": 0.21, "car": 0.39}	error 0.506

test intercity-probability-v2-99

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 50 thousand dollars. air: cost 94 dollars; waiting 64 min; in-vehicle 231 min; generalized cost 129 dollars. train: cost 79 dollars; waiting 44 min; in-vehicle 949 min; generalized cost 223 dollars. bus: cost 32 dollars; waiting 40 min; in-vehicle 1110 min; generalized cost 201 dollars. car: cost 13 dollars; waiting 0 min; in-vehicle 942 min; generalized cost 156 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.35, "train": 0.15, "bus": 0.15, "car": 0.35}	error 0.99
Llama 3.3	{"air": 0.421, "train": 0.143, "bus": 0.078, "car": 0.358}	error 1.18
Qwen · off	{"air": 0.05, "train": 0.05, "bus": 0.15, "car": 0.75}	error 1.29
Qwen · on	{"air": 0.45, "train": 0.11, "bus": 0.15, "car": 0.29}	error 1.02

test intercity-probability-v2-100

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 70 thousand dollars. air: cost 92 dollars; waiting 64 min; in-vehicle 203 min; generalized cost 123 dollars. train: cost 77 dollars; waiting 44 min; in-vehicle 961 min; generalized cost 223 dollars. bus: cost 46 dollars; waiting 53 min; in-vehicle 951 min; generalized cost 190 dollars. car: cost 17 dollars; waiting 0 min; in-vehicle 780 min; generalized cost 135 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.35, "train": 0.15, "bus": 0.1, "car": 0.4}	error 0.515
Llama 3.3	{"air": 0.43, "train": 0.06, "bus": 0.15, "car": 0.36}	error 0.621
Qwen · off	{"air": 0.0001, "train": 0.0001, "bus": 0.0001, "car": 0.9997}	error 1.2e-07
Qwen · on	{"air": 0.58, "train": 0.01, "bus": 0.04, "car": 0.37}	error 0.735

test intercity-probability-v2-102

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 50 thousand dollars. air: cost 75 dollars; waiting 64 min; in-vehicle 153 min; generalized cost 99 dollars. train: cost 64 dollars; waiting 44 min; in-vehicle 900 min; generalized cost 201 dollars. bus: cost 45 dollars; waiting 53 min; in-vehicle 890 min; generalized cost 180 dollars. car: cost 13 dollars; waiting 0 min; in-vehicle 720 min; generalized cost 122 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.45, "train": 0.1, "bus": 0.15, "car": 0.3}	error 0.725
Llama 3.3	{"air": 0.55, "train": 0.15, "bus": 0.1, "car": 0.2}	error 0.975
Qwen · off	{"air": 0.0001, "train": 0.0001, "bus": 0.0001, "car": 0.9997}	error 1.2e-07
Qwen · on	{"air": 0.5104, "train": 0.0664, "bus": 0.101, "car": 0.3222}	error 0.735

test intercity-probability-v2-105

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 27 thousand dollars. air: cost 108 dollars; waiting 64 min; in-vehicle 187 min; generalized cost 136 dollars. train: cost 90 dollars; waiting 44 min; in-vehicle 932 min; generalized cost 231 dollars. bus: cost 45 dollars; waiting 53 min; in-vehicle 922 min; generalized cost 185 dollars. car: cost 20 dollars; waiting 0 min; in-vehicle 1440 min; generalized cost 238 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.35, "train": 0.15, "bus": 0.25, "car": 0.25}	error 0.77
Llama 3.3	{"air": 0.55, "train": 0.15, "bus": 0.2, "car": 0.1}	error 1.18
Qwen · off	{"air": 0.45, "train": 0.15, "bus": 0.25, "car": 0.15}	error 1.01
Qwen · on	{"air": 0.75, "train": 0.04, "bus": 0.17, "car": 0.04}	error 1.51

test intercity-probability-v2-108

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 40 thousand dollars. air: cost 78 dollars; waiting 64 min; in-vehicle 146 min; generalized cost 100 dollars. train: cost 66 dollars; waiting 44 min; in-vehicle 903 min; generalized cost 203 dollars. bus: cost 43 dollars; waiting 53 min; in-vehicle 893 min; generalized cost 178 dollars. car: cost 11 dollars; waiting 0 min; in-vehicle 870 min; generalized cost 143 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.35, "train": 0.15, "bus": 0.1, "car": 0.4}	error 0.515
Llama 3.3	{"air": 0.55, "train": 0.05, "bus": 0.1, "car": 0.3}	error 0.805
Qwen · off	{"air": 0.001, "train": 0.001, "bus": 0.001, "car": 0.997}	error 1.2e-05
Qwen · on	{"air": 0.49, "train": 0.1, "bus": 0.15, "car": 0.26}	error 0.82

test intercity-probability-v2-110

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 40 thousand dollars. air: cost 78 dollars; waiting 64 min; in-vehicle 175 min; generalized cost 105 dollars. train: cost 67 dollars; waiting 44 min; in-vehicle 932 min; generalized cost 208 dollars. bus: cost 44 dollars; waiting 53 min; in-vehicle 922 min; generalized cost 183 dollars. car: cost 12 dollars; waiting 0 min; in-vehicle 720 min; generalized cost 121 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.45, "train": 0.05, "bus": 0.05, "car": 0.45}	error 0.51
Llama 3.3	{"air": 0.43, "train": 0.03, "bus": 0.04, "car": 0.5}	error 0.437
Qwen · off	{"air": 0.001, "train": 0.001, "bus": 0.001, "car": 0.997}	error 1.2e-05
Qwen · on	{"air": 0.601, "train": 0.016, "bus": 0.039, "car": 0.344}	error 0.793

test intercity-probability-v2-116

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 45 thousand dollars. air: cost 66 dollars; waiting 40 min; in-vehicle 105 min; generalized cost 77 dollars. train: cost 31 dollars; waiting 34 min; in-vehicle 372 min; generalized cost 71 dollars. bus: cost 25 dollars; waiting 35 min; in-vehicle 417 min; generalized cost 70 dollars. car: cost 18 dollars; waiting 0 min; in-vehicle 327 min; generalized cost 54 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.08, "train": 0.24, "bus": 0.26, "car": 0.42}	error 1.15
Llama 3.3	{"air": 0.2, "train": 0.15, "bus": 0.1, "car": 0.55}	error 0.975
Qwen · off	{"air": 0.05, "train": 0.15, "bus": 0.15, "car": 0.65}	error 1.37
Qwen · on	{"air": 0.206, "train": 0.232, "bus": 0.236, "car": 0.326}	error 0.846

test intercity-probability-v2-118

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 6 thousand dollars. air: cost 129 dollars; waiting 69 min; in-vehicle 185 min; generalized cost 149 dollars. train: cost 67 dollars; waiting 34 min; in-vehicle 933 min; generalized cost 168 dollars. bus: cost 54 dollars; waiting 20 min; in-vehicle 820 min; generalized cost 143 dollars. car: cost 38 dollars; waiting 0 min; in-vehicle 894 min; generalized cost 135 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.22, "train": 0.18, "bus": 0.28, "car": 0.32}	error 0.702
Llama 3.3	{"air": 0.141, "train": 0.105, "bus": 0.143, "car": 0.611}	error 1.14
Qwen · off	{"air": 0.24, "train": 0.18, "bus": 0.28, "car": 0.3}	error 0.698
Qwen · on	{"air": 0.25, "train": 0.2, "bus": 0.26, "car": 0.29}	error 0.734

test intercity-probability-v2-124

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 8 thousand dollars. air: cost 95 dollars; waiting 35 min; in-vehicle 155 min; generalized cost 119 dollars. train: cost 45 dollars; waiting 44 min; in-vehicle 930 min; generalized cost 186 dollars. bus: cost 43 dollars; waiting 53 min; in-vehicle 920 min; generalized cost 183 dollars. car: cost 23 dollars; waiting 0 min; in-vehicle 860 min; generalized cost 153 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.45, "train": 0.15, "bus": 0.15, "car": 0.25}	error 0.41
Llama 3.3	{"air": 0.4, "train": 0.1, "bus": 0.1, "car": 0.4}	error 0.54
Qwen · off	{"air": 0.001, "train": 0.001, "bus": 0.001, "car": 0.997}	error 1.99
Qwen · on	{"air": 0.35, "train": 0.13, "bus": 0.12, "car": 0.4}	error 0.614

test intercity-probability-v2-126

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 45 thousand dollars. air: cost 103 dollars; waiting 64 min; in-vehicle 170 min; generalized cost 129 dollars. train: cost 88 dollars; waiting 44 min; in-vehicle 889 min; generalized cost 222 dollars. bus: cost 35 dollars; waiting 30 min; in-vehicle 770 min; generalized cost 152 dollars. car: cost 18 dollars; waiting 0 min; in-vehicle 905 min; generalized cost 155 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.24, "train": 0.16, "bus": 0.32, "car": 0.28}	error 0.624
Llama 3.3	{"air": 0.43, "train": 0.07, "bus": 0.15, "car": 0.35}	error 1.03
Qwen · off	{"air": 0.05, "train": 0.02, "bus": 0.45, "car": 0.48}	error 0.536
Qwen · on	{"air": 0.48, "train": 0.07, "bus": 0.23, "car": 0.22}	error 0.877

test intercity-probability-v2-134

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 8 thousand dollars. air: cost 103 dollars; waiting 69 min; in-vehicle 149 min; generalized cost 119 dollars. train: cost 45 dollars; waiting 34 min; in-vehicle 892 min; generalized cost 142 dollars. bus: cost 25 dollars; waiting 25 min; in-vehicle 730 min; generalized cost 104 dollars. car: cost 37 dollars; waiting 0 min; in-vehicle 882 min; generalized cost 133 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.28, "train": 0.18, "bus": 0.35, "car": 0.19}	error 0.569
Llama 3.3	{"air": 0.43, "train": 0.06, "bus": 0.15, "car": 0.36}	error 1.04
Qwen · off	{"air": 0.15, "train": 0.1, "bus": 0.45, "car": 0.3}	error 0.425
Qwen · on	{"air": 0.27, "train": 0.15, "bus": 0.39, "car": 0.19}	error 0.504

test intercity-probability-v2-135

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 60 thousand dollars. air: cost 103 dollars; waiting 64 min; in-vehicle 160 min; generalized cost 127 dollars. train: cost 89 dollars; waiting 44 min; in-vehicle 987 min; generalized cost 239 dollars. bus: cost 44 dollars; waiting 53 min; in-vehicle 977 min; generalized cost 192 dollars. car: cost 34 dollars; waiting 0 min; in-vehicle 660 min; generalized cost 134 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.35, "train": 0.1, "bus": 0.05, "car": 0.5}	error 0.385
Llama 3.3	{"air": 0.401, "train": 0.073, "bus": 0.104, "car": 0.422}	error 0.511
Qwen · off	{"air": 0.35, "train": 0.05, "bus": 0.15, "car": 0.45}	error 0.45
Qwen · on	{"air": 0.44, "train": 0.05, "bus": 0.12, "car": 0.39}	error 0.583

test intercity-probability-v2-136

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 12 thousand dollars. air: cost 114 dollars; waiting 64 min; in-vehicle 161 min; generalized cost 138 dollars. train: cost 60 dollars; waiting 44 min; in-vehicle 1031 min; generalized cost 217 dollars. bus: cost 58 dollars; waiting 53 min; in-vehicle 1021 min; generalized cost 213 dollars. car: cost 19 dollars; waiting 0 min; in-vehicle 720 min; generalized cost 128 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.28, "train": 0.15, "bus": 0.14, "car": 0.43}	error 0.445
Llama 3.3	{"air": 0.41, "train": 0.03, "bus": 0.02, "car": 0.54}	error 0.381
Qwen · off	{"air": 0.05, "train": 0.02, "bus": 0.03, "car": 0.9}	error 0.0138
Qwen · on	{"air": 0.358, "train": 0.11, "bus": 0.116, "car": 0.416}	error 0.495

test intercity-probability-v2-147

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 4 thousand dollars. air: cost 107 dollars; waiting 69 min; in-vehicle 152 min; generalized cost 124 dollars. train: cost 33 dollars; waiting 30 min; in-vehicle 755 min; generalized cost 115 dollars. bus: cost 44 dollars; waiting 35 min; in-vehicle 882 min; generalized cost 140 dollars. car: cost 48 dollars; waiting 0 min; in-vehicle 845 min; generalized cost 140 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.28, "train": 0.32, "bus": 0.2, "car": 0.2}	error 0.621
Llama 3.3	{"air": 0.43, "train": 0.29, "bus": 0.14, "car": 0.14}	error 0.728
Qwen · off	{"air": 0.25, "train": 0.45, "bus": 0.15, "car": 0.15}	error 0.41
Qwen · on	{"air": 0.28, "train": 0.37, "bus": 0.175, "car": 0.175}	error 0.537

test intercity-probability-v2-152

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 50 thousand dollars. air: cost 102 dollars; waiting 60 min; in-vehicle 250 min; generalized cost 129 dollars. train: cost 112 dollars; waiting 34 min; in-vehicle 997 min; generalized cost 220 dollars. bus: cost 67 dollars; waiting 35 min; in-vehicle 952 min; generalized cost 170 dollars. car: cost 43 dollars; waiting 0 min; in-vehicle 971 min; generalized cost 148 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.35, "train": 0.05, "bus": 0.15, "car": 0.45}	error 0.65
Llama 3.3	{"air": 0.35, "train": 0.05, "bus": 0.2, "car": 0.4}	error 0.625
Qwen · off	{"air": 0.001, "train": 0.001, "bus": 0.001, "car": 0.997}	error 1.99
Qwen · on	{"air": 0.36, "train": 0.12, "bus": 0.22, "car": 0.3}	error 0.562

test intercity-probability-v2-156

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 35 thousand dollars. air: cost 74 dollars; waiting 45 min; in-vehicle 70 min; generalized cost 85 dollars. train: cost 26 dollars; waiting 44 min; in-vehicle 361 min; generalized cost 81 dollars. bus: cost 21 dollars; waiting 53 min; in-vehicle 406 min; generalized cost 82 dollars. car: cost 4 dollars; waiting 0 min; in-vehicle 315 min; generalized cost 52 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.12, "train": 0.28, "bus": 0.25, "car": 0.35}	error 1.04
Llama 3.3	{"air": 0.41, "train": 0.25, "bus": 0.14, "car": 0.2}	error 0.47
Qwen · off	{"air": 0.05, "train": 0.15, "bus": 0.1, "car": 0.7}	error 1.42
Qwen · on	{"air": 0.04, "train": 0.07, "bus": 0.06, "car": 0.83}	error 1.62

test intercity-probability-v2-157

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 60 thousand dollars. air: cost 165 dollars; waiting 75 min; in-vehicle 180 min; generalized cost 192 dollars. train: cost 98 dollars; waiting 44 min; in-vehicle 967 min; generalized cost 245 dollars. bus: cost 53 dollars; waiting 53 min; in-vehicle 922 min; generalized cost 193 dollars. car: cost 26 dollars; waiting 0 min; in-vehicle 947 min; generalized cost 170 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.24, "train": 0.14, "bus": 0.26, "car": 0.36}	error 0.794
Llama 3.3	{"air": 0.401, "train": 0.104, "bus": 0.157, "car": 0.338}	error 0.509
Qwen · off	{"air": 0.24, "train": 0.18, "bus": 0.25, "car": 0.33}	error 0.781
Qwen · on	{"air": 0.65, "train": 0.08, "bus": 0.12, "car": 0.15}	error 0.166

test intercity-probability-v2-160

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 40 thousand dollars. air: cost 75 dollars; waiting 45 min; in-vehicle 75 min; generalized cost 96 dollars. train: cost 33 dollars; waiting 44 min; in-vehicle 418 min; generalized cost 96 dollars. bus: cost 28 dollars; waiting 53 min; in-vehicle 463 min; generalized cost 98 dollars. car: cost 5 dollars; waiting 0 min; in-vehicle 291 min; generalized cost 49 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.25, "train": 0.25, "bus": 0.15, "car": 0.35}	error 0.77
Llama 3.3	{"air": 0.35, "train": 0.25, "bus": 0.1, "car": 0.3}	error 0.585
Qwen · off	{"air": 0.25, "train": 0.25, "bus": 0.15, "car": 0.35}	error 0.77
Qwen · on	{"air": 0.181, "train": 0.181, "bus": 0.174, "car": 0.464}	error 0.949

test intercity-probability-v2-169

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 30 thousand dollars. air: cost 81 dollars; waiting 69 min; in-vehicle 95 min; generalized cost 91 dollars. train: cost 70 dollars; waiting 34 min; in-vehicle 610 min; generalized cost 136 dollars. bus: cost 31 dollars; waiting 35 min; in-vehicle 604 min; generalized cost 96 dollars. car: cost 30 dollars; waiting 0 min; in-vehicle 440 min; generalized cost 78 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.26, "train": 0.14, "bus": 0.25, "car": 0.35}	error 0.572
Llama 3.3	{"air": 0.23, "train": 0.11, "bus": 0.16, "car": 0.5}	error 0.341
Qwen · off	{"air": 0.05, "train": 0.02, "bus": 0.18, "car": 0.75}	error 0.0978
Qwen · on	{"air": 0.189, "train": 0.002, "bus": 0.115, "car": 0.694}	error 0.143

test intercity-probability-v2-171

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 50 thousand dollars. air: cost 82 dollars; waiting 64 min; in-vehicle 159 min; generalized cost 106 dollars. train: cost 71 dollars; waiting 44 min; in-vehicle 765 min; generalized cost 187 dollars. bus: cost 32 dollars; waiting 53 min; in-vehicle 759 min; generalized cost 147 dollars. car: cost 13 dollars; waiting 0 min; in-vehicle 490 min; generalized cost 87 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.35, "train": 0.05, "bus": 0.1, "car": 0.5}	error 0.385
Llama 3.3	{"air": 0.417, "train": 0.063, "bus": 0.083, "car": 0.437}	error 0.502
Qwen · off	{"air": 0.05, "train": 0.02, "bus": 0.13, "car": 0.8}	error 0.0598
Qwen · on	{"air": 0.32, "train": 0.04, "bus": 0.12, "car": 0.52}	error 0.349

test intercity-probability-v2-185

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 35 thousand dollars. air: cost 58 dollars; waiting 64 min; in-vehicle 74 min; generalized cost 69 dollars. train: cost 21 dollars; waiting 30 min; in-vehicle 295 min; generalized cost 66 dollars. bus: cost 24 dollars; waiting 53 min; in-vehicle 389 min; generalized cost 83 dollars. car: cost 7 dollars; waiting 0 min; in-vehicle 315 min; generalized cost 55 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.24, "train": 0.31, "bus": 0.12, "car": 0.33}	error 0.657
Llama 3.3	{"air": 0.35, "train": 0.25, "bus": 0.1, "car": 0.3}	error 0.785
Qwen · off	{"air": 0.15, "train": 0.25, "bus": 0.1, "car": 0.5}	error 0.845
Qwen · on	{"air": 0.13, "train": 0.31, "bus": 0.09, "car": 0.47}	error 0.722

test intercity-probability-v2-188

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 30 thousand dollars. air: cost 61 dollars; waiting 10 min; in-vehicle 80 min; generalized cost 73 dollars. train: cost 24 dollars; waiting 44 min; in-vehicle 350 min; generalized cost 77 dollars. bus: cost 19 dollars; waiting 53 min; in-vehicle 395 min; generalized cost 79 dollars. car: cost 4 dollars; waiting 0 min; in-vehicle 314 min; generalized cost 52 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.24, "train": 0.22, "bus": 0.18, "car": 0.36}	error 0.788
Llama 3.3	{"air": 0.41, "train": 0.26, "bus": 0.15, "car": 0.18}	error 0.471
Qwen · off	{"air": 0.15, "train": 0.12, "bus": 0.08, "car": 0.65}	error 1.17
Qwen · on	{"air": 0.13, "train": 0.09, "bus": 0.08, "car": 0.7}	error 1.26

test intercity-probability-v2-190

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 60 thousand dollars. air: cost 58 dollars; waiting 69 min; in-vehicle 73 min; generalized cost 66 dollars. train: cost 31 dollars; waiting 34 min; in-vehicle 324 min; generalized cost 66 dollars. bus: cost 25 dollars; waiting 35 min; in-vehicle 334 min; generalized cost 61 dollars. car: cost 18 dollars; waiting 0 min; in-vehicle 240 min; generalized cost 44 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.12, "train": 0.18, "bus": 0.25, "car": 0.45}	error 0.412
Llama 3.3	{"air": 0.15, "train": 0.15, "bus": 0.2, "car": 0.5}	error 0.335
Qwen · off	{"air": 0.05, "train": 0.15, "bus": 0.2, "car": 0.6}	error 0.225
Qwen · on	{"air": 0.28, "train": 0.13, "bus": 0.14, "car": 0.45}	error 0.417

test intercity-probability-v2-193

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 60 thousand dollars. air: cost 76 dollars; waiting 20 min; in-vehicle 95 min; generalized cost 86 dollars. train: cost 33 dollars; waiting 34 min; in-vehicle 344 min; generalized cost 70 dollars. bus: cost 27 dollars; waiting 35 min; in-vehicle 389 min; generalized cost 69 dollars. car: cost 13 dollars; waiting 0 min; in-vehicle 315 min; generalized cost 47 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.12, "train": 0.24, "bus": 0.24, "car": 0.4}	error 1.05
Llama 3.3	{"air": 0.23, "train": 0.15, "bus": 0.12, "car": 0.5}	error 0.88
Qwen · off	{"air": 0.05, "train": 0.15, "bus": 0.15, "car": 0.65}	error 1.37
Qwen · on	{"air": 0.016, "train": 0.081, "bus": 0.09, "car": 0.813}	error 1.64

test intercity-probability-v2-199

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 70 thousand dollars. air: cost 64 dollars; waiting 5 min; in-vehicle 80 min; generalized cost 76 dollars. train: cost 30 dollars; waiting 44 min; in-vehicle 348 min; generalized cost 83 dollars. bus: cost 24 dollars; waiting 53 min; in-vehicle 393 min; generalized cost 84 dollars. car: cost 7 dollars; waiting 0 min; in-vehicle 291 min; generalized cost 51 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.32, "train": 0.24, "bus": 0.15, "car": 0.29}	error 0.627
Llama 3.3	{"air": 0.43, "train": 0.24, "bus": 0.12, "car": 0.21}	error 0.441
Qwen · off	{"air": 0.05, "train": 0.08, "bus": 0.07, "car": 0.8}	error 1.55
Qwen · on	{"air": 0.071, "train": 0.035, "bus": 0.032, "car": 0.862}	error 1.61

test intercity-probability-v2-204

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 20 thousand dollars. air: cost 60 dollars; waiting 69 min; in-vehicle 66 min; generalized cost 67 dollars. train: cost 34 dollars; waiting 34 min; in-vehicle 352 min; generalized cost 72 dollars. bus: cost 37 dollars; waiting 10 min; in-vehicle 250 min; generalized cost 64 dollars. car: cost 13 dollars; waiting 0 min; in-vehicle 307 min; generalized cost 46 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.08, "train": 0.12, "bus": 0.25, "car": 0.55}	error 0.886
Llama 3.3	{"air": 0.15, "train": 0.05, "bus": 0.1, "car": 0.7}	error 1.32
Qwen · off	{"air": 0.15, "train": 0.12, "bus": 0.25, "car": 0.48}	error 0.83
Qwen · on	{"air": 0.12, "train": 0.08, "bus": 0.15, "car": 0.65}	error 1.17

test intercity-probability-v2-209

A traveller in the 1987 Sydney–Canberra–Melbourne non-business intercity sample has household income 20 thousand dollars. air: cost 81 dollars; waiting 69 min; in-vehicle 124 min; generalized cost 94 dollars. train: cost 35 dollars; waiting 34 min; in-vehicle 605 min; generalized cost 100 dollars. bus: cost 31 dollars; waiting 35 min; in-vehicle 599 min; generalized cost 96 dollars. car: cost 27 dollars; waiting 0 min; in-vehicle 510 min; generalized cost 82 dollars. Estimate probabilities for air, train, bus, car; values must sum to 1. This is a choice-based sample, not population mode shares.
Give your best estimate even if you are uncertain. Return only a JSON object mapping each of air, train, bus, car to its probability; the probabilities must sum to 1. Do not return null and do not add explanations.

Model	Answer given
Gemma 4	{"air": 0.25, "train": 0.2, "bus": 0.2, "car": 0.35}	error 0.565
Llama 3.3	{"air": 0.23, "train": 0.05, "bus": 0.06, "car": 0.66}	error 0.175
Qwen · off	{"air": 0.24, "train": 0.22, "bus": 0.23, "car": 0.31}	error 0.635
Qwen · on	{"air": 0.24, "train": 0.2, "bus": 0.22, "car": 0.34}	error 0.582