2025 · Paper 2 · Mathematics
Question 11
The printed question, the official key, and each model’s JSON answer plus the reasoning it wrote.
MathematicsPaper 2Numerical
Q11
Official 0.27 – 0.33
Model answers
Claude Fable 5.1
Anthropic
Correct4 / 4
0.3
Claude Fable 5.1 reasoning
Let P(M1)=2/5, P(M2)=2/5, P(M3)=1/5. Let P(D|M1)=0.15, P(D|M2)=p, P(D|M3)=q. Total defective: P(D) = 0.2. Given P(M2|D) = 2/5: P(M2 ∩ D)/P(D) = (2/5)p / 0.2 = 2/5 ⇒ (2/5)p = 0.08 ⇒ p = 0.2. Total probability: 0.2 = (2/5)(0.15) + (2/5)(0.2) + (1/5)q 0.2 = 0.06 + 0.08 + q/5 q/5 = 0.06 ⇒ q = 0.3
GPT 6 Astra
OpenAI
Correct4 / 4
0.3
GPT 6 Astra reasoning
No written reasoning was returned for this item.
GPT 5.6 Luna
OpenAI
Correct4 / 4
0.3
GPT 5.6 Luna reasoning
No written reasoning was returned for this item.